Exhibit 4.1

AMENDMENT NO. 2

TO

RIGHTS AGREEMENT

This AMENDMENT NO. 2 (this “ Amendment ”) to the Rights Agreement, dated as of July 22, 2018, by and between Papa John’s International, Inc., a Delaware corporation (the “ Company ”), and Computershare Trust Company, N.A., as rights agent (the “ Rights Agent ”), as amended by Amendment No. 1 to the Rights Agreement, dated as of February 3, 2019 (as amended, the “ Rights Agreement ”), is entered into as of March 6, 2019.  Capitalized terms used in this Amendment and not otherwise defined herein shall have the meanings given to them in the Rights Agreement.

WHEREAS , pursuant to Section 27 of the Rights Agreement, the Company may from time to time supplement or amend the Rights Agreement, in accordance with the provisions of Section 27 thereof;

WHEREAS , the Board has determined that it is in the best interests of the Company and its stockholders to amend the Rights Agreement pursuant to and in accordance with Section 27 thereof to (a) extend the term of the Rights Agreement from July 22, 2019 to March 6, 2022, (b) increase the beneficial ownership threshold at which a person becomes an Acquiring Person from 15% to 20%, (c) remove the “acting in concert” provision, and (d) include a “qualifying offer” provision;

WHEREAS , no Person has become an Acquiring Person under the Rights Agreement; and

WHEREAS , pursuant to Section 27 of the Rights Agreement, the Company hereby directs the Rights Agent that the Rights Agreement shall be amended as set forth in this Amendment.

NOW, THEREFORE , in consideration of the foregoing and the mutual agreements herein set forth, the parties hereto hereby agree to amend the Rights Agreement as follows:

1.               Section 1(a) is hereby amended by deleting each reference to “15%” and replacing each such reference with a reference to “20%”.

2.               Section 1(b) is hereby amended and restated in its entirety to read as follows:

“(b)   Reserved.”

3.               Subparagraph (iii) of Section 1(d) is hereby amended by deleting the phrase “is (A) Acting in Concert, or (B)”.

4.               Subparagraphs (ii) and (iii) of Section 1(d) are hereby amended by deleting the references to “this paragraph (c)” and replacing each such reference with a reference to “this paragraph (d)”.

5.               Section 1(h) is hereby amended and restated in its entirety to read as follows:

“(h)  “ Certificate of Incorporation ” shall mean the Amended and Restated Certificate of Incorporation of the Company, dated May 15, 2014, as filed with the Office of the Secretary of State of the State of Delaware (the “ Secretary of State ”), and together with the Certificate of Designation of the Preferred Stock of the Company, as filed with the Secretary of State on July 23, 2018 and attached hereto as Exhibit A (the “ Certificate of Designation ”) and the Certificate of Designation of the Series B Convertible Preferred Stock, as filed with the Secretary of State on February 4, 2019 (the “ Series B Certificate of Designation ”), as the same may hereafter be amended or restated.”

6.               Section 1(l) is hereby amended by deleting the reference to “the Beneficial Owner of 15% or more of the outstanding shares of Common Stock” and replacing it with a reference to “an Acquiring Person”.

7.               The definition of “ Starboard Exempt Party ” in Section 1 is hereby amended and restated in its entirety to read as follows:

““ Starboard Exempt Party ” shall mean each of the Starboard Investors and their respective Affiliates and Associates, including any accounts managed by the Starboard Investors or any of their respective Affiliates or Associates, so long as each such Person is not, at any time, the Beneficial Owner of any shares of Common Stock that are not Starboard Shares; provided , however , that such Persons shall not cease to be a Starboard Exempt Party and become an Acquiring Person as the result of:

(i)              a dividend or distribution paid or made by the Company on the outstanding Common Stock or pursuant to a split or subdivision of the outstanding Common Stock; or

(ii)           any unilateral grant of any security by the Company, or through the exercise of any options, warrants, rights or similar interests (including restricted stock) granted by the Company to such Starboard Exempt Party.”

8.               Section 1 is hereby amended by adding the following definitions in the appropriate alphabetical order:

“ Definitive Acquisition Agreement ” shall mean any definitive written agreement entered into by the Company that is conditioned on the approval by the holders of not less than a majority of the outstanding shares of Common Stock at a meeting of the stockholders of the Company with respect to (i) a merger, consolidation, recapitalization, reorganization, share exchange, business combination or similar transaction involving the Company or (ii) the acquisition in

any manner, directly or indirectly, of more than 50% of the consolidated total assets (including, without limitation, equity securities of its subsidiaries) of the Company and its Subsidiaries.

“ Exemption Date ” shall have the meaning set forth in Section 23(c) hereof.

“ Independent Directors ” shall mean members of the Board who are not officers, employees or Affiliates of the Company (or designees of such Affiliates).

“ Outside Meeting Date ” shall have the meaning set forth in Section 23(c) hereof.

“ Qualifying Offer ” shall mean an offer determined by a majority of Independent Directors to have each of the following characteristics:

(i) a fully financed, all cash tender offer for all of the outstanding Common Stock, or an exchange offer offering shares of common stock of the offeror, or a combination thereof, in each such case for any and all of the outstanding Common Stock (whether such shares are outstanding at the commencement of the offer or become outstanding thereafter upon the exercise or conversion of options or other securities that are outstanding at the commencement of the offer) at the same per share consideration;

(ii) an offer that has commenced within the meaning of Rule 14d-2(a) under the Exchange Act;

(iii) an offer that, within twenty (20) Business Days after the commencement date of such offer (or within ten (10) Business Days after any increase in the offer consideration), does not result in a nationally recognized investment banking firm retained by the Board rendering an opinion to the Board that the consideration being offered to the holders of the Common Stock is either inadequate or unfair, from a financial standpoint, to the stockholders of the Company (other than the Acquiring Person and its Affiliates);

(iv) an offer that is subject to only the minimum tender condition described below in subparagraph (vii) of this definition and other customary terms and conditions, which conditions shall not include any financing, funding or similar conditions or any requirements with respect to the offeror or its agents or any Person being permitted any due diligence with respect to the books, records, management, accountants or other outside advisors of the Company;

(v) an offer pursuant to which the Company has received an irrevocable written commitment of the offeror that the offer will remain open for at least ninety (90) Business Days and, if a Special Meeting is duly requested in accordance with Section 23(c), for at least ten (10) Business Days after the date of the Special Meeting or, if no Special Meeting is held within ninety (90) Business Days following receipt of the Special

Meeting Demand in accordance with Section 23(c), for at least ten (10) Business Days following such ninety (90) Business Day period;

(vi) an offer pursuant to which the Company has received an irrevocable written commitment of the offeror that, in addition to the minimum time periods specified above in subparagraph (v) of this definition, the offer, if it is otherwise to expire prior thereto, will be extended for at least twenty (20) Business Days after any increase in the consideration being offered or after any bona fide alternative offer is commenced within the meaning of Rule 14d-2(a) under the Exchange Act; provided , however , that such offer need not remain open, as a result of subparagraph (v) of this definition and this subparagraph (vi), beyond (A) the time that any other offer satisfying the criteria for a Qualifying Offer is then required to be kept open under such subparagraph (v) of this definition and this subparagraph (vi) or (B) the expiration date, as such date may be extended by public announcement (with prompt written notice to the Rights Agent) in compliance with Rule 14e-1 under the Exchange Act, of any other tender or exchange offer for the Common Stock with respect to which the Board has agreed to redeem the Rights immediately prior to acceptance for payment of Common Stock thereunder (unless such other offer is terminated prior to its expiration without any Common Stock having been purchased thereunder) or (C) one Business Day after the stockholder vote with respect to the approval of any Definitive Acquisition Agreement has been officially determined and certified by the inspectors of elections;

(vii) an offer that is conditioned on a minimum of at least a majority of (A) the shares of Common Stock of the Company outstanding on a fully-diluted basis; and (B) the outstanding shares of Common Stock of the Company not held by the offeror (or such offeror’s Affiliates and Associates) being tendered and not withdrawn as of the offer’s expiration date, which condition shall not be waivable;

(viii) an offer pursuant to which the Company has received an irrevocable written commitment of the offeror to consummate, as promptly as practicable upon successful completion of the offer, a second-step transaction whereby all Common Stock not purchased in the offer will be acquired at the same consideration per share actually paid pursuant to the offer, subject to stockholders’ statutory appraisal rights, if any;

(ix) an offer pursuant to which the Company and its stockholders have received an irrevocable written commitment of the offeror that no amendments will be made to the offer to reduce the consideration being offered or to otherwise change the terms of the offer in a way that is adverse to a tendering stockholder (other than extensions of the offer consistent with the terms hereof);

(x) if the offer includes shares of common stock of the offeror, an offer pursuant to which (A) the offeror shall permit representatives of the Company (including a nationally recognized investment banking firm retained by the Board and legal counsel and an accounting firm designated by the Company) to have access to such offeror’s books,

records, management, accountants, financial advisors, counsel and any other appropriate outside advisers for the purposes of permitting such representatives to conduct a due diligence review of the offeror in order to permit the Board to evaluate the offer and make an informed decision and, if requested by the Board, to permit such investment banking firm (relying as appropriate on the advice of such legal counsel) to be able to render an opinion to the Board with respect to whether the consideration being offered to the stockholders of the Company is fair from a financial point of view, and (B) within ten (10) Business Days after such representatives of the Company (including a nationally-recognized investment banking firm retained by the Board, legal counsel and an accounting firm designated by the Company) shall have notified the Company and the offeror that they had completed such due diligence review to their satisfaction (or, following completion of such due diligence review, within ten (10) Business Days after any increase in the consideration being offered), such investment banking firm does not render an opinion to the Board of the Company that the consideration being offered to the stockholders of the Company is either unfair or inadequate and such investment banking firm does not, after the expiration of such ten (10) Business Day period, render an opinion to the Board that the consideration being offered to the stockholders of the Company has become either unfair or inadequate based on a subsequent disclosure or discovery of a development or developments that have had or are reasonably likely to have an adverse effect on the value of the common stock of the offeror;

(xi) an offer (other than an offer consisting solely of cash consideration) pursuant to which the Company has received the written representation and certification of the offeror and the written representations and certifications of the offeror’s Chief Executive Officer and Chief Financial Officer, acting in such capacities, that (A) all facts about the offeror that would be material to making an investor’s decision to accept the offer have been fully and accurately disclosed as of the date of the commencement of the offer within the meaning of Rule 14d-2(a) under the Exchange Act, (B) all such new facts will be fully and accurately disclosed on a prompt basis during the entire period during which the offer remains open, and (C) all required Exchange Act reports will be filed by the offeror in a timely manner during such period;

(xii) if the offer includes non-cash consideration (A) the non-cash portion of the consideration offered must consist solely of common stock of a Person that is a publicly-owned United States corporation, (B) such common stock must be freely tradable and listed or admitted to trading on either the NYSE or the Nasdaq, (C) no stockholder approval of the issuer of such common stock is required to issue such common stock, or, if such approval is required, such approval has already been obtained, (D) such issuer of such common stock has no other class of voting stock or other voting securities, and (E) the issuer of such common stock meets the registrant eligibility requirements for use of Form S-3 for registering securities under the Securities Act, including the filing of all required Exchange Act reports in a timely manner during the twelve calendar months prior to the date of commencement of such offer; and

(xiii) an offer that is otherwise in the best interests of the Company and its stockholders.

For the purposes of this definition of “Qualifying Offer,” “ fully financed ” shall mean that the offeror has sufficient funds for the offer and related expenses, which shall be evidenced by (i) firm, unqualified, written commitments from responsible financial institutions having the necessary financial capacity, accepted by the offeror, to provide funds for such offer, subject only to customary terms and conditions, which conditions shall not include any requirements with respect to such financial institutions or any other Person being permitted any due diligence with respect to the books, records, management, accountants and other outside advisors of the Company, (ii) cash or cash equivalents then available to the offeror, set apart and maintained solely for the purpose of funding the offer with an irrevocable written commitment being provided by the offeror to the Company to maintain such availability until the offer is consummated or withdrawn or (iii) a combination of the foregoing; which evidence has been provided to the Company prior to, or upon, commencement of the offer and is reasonably satisfactory to the Board. If an offer becomes a Qualifying Offer in accordance with this definition, but subsequently ceases to be a Qualifying Offer as a result of the failure at a later date to continue to satisfy any of the requirements of this definition, such offer shall cease to be a Qualifying Offer and the provisions of Section 23(c) shall no longer be applicable to such offer, provided, that an Exemption Date shall not have already occurred with respect to such Qualifying Offer pursuant to Section 23(c).

“ Qualifying Offer Resolution ” shall have the meaning set forth in Section 23(c) hereof.

“ Special Meeting ” shall have the meaning set forth in Section 23(c) hereof.

“ Special Meeting Demand ” shall have the meaning set forth in Section 23(c) hereof.

“ Special Meeting Period ” shall have the meaning set forth in Section 23(c) hereof.

“ Series B Preferred Stock ” shall mean the Series B Convertible Preferred Stock, $0.01 par value per share, of the Company.

“ Series B-1 Preferred Stock ” shall mean the Series B-1 Preferred Stock, $0.01 par value per share, of the Company.

“ Series B-2 Preferred Stock ” shall mean the Series B-2 Preferred Stock, $0.01 par value per share, of the Company.

9.               Section 7(a) is hereby amended by deleting the reference to “July 22, 2019” and replacing it with a reference to “March 6, 2022”.

10.        Section 23 is hereby amended by adding the following paragraph as paragraph (c):

“(c)         Exempting a Qualifying Offer from this Agreement .

(i) In the event the Company receives a Qualifying Offer and the Board has not redeemed the outstanding Rights or exempted such offer from the terms of this Agreement or called a special meeting of stockholders by the end of the ninetieth (90th) Business Day following the commencement of such Qualifying Offer within the meaning of Rule 14d-2(a) under the Exchange Act, for the purpose of voting on whether to exempt such Qualifying Offer from the terms of this Agreement, provided, that such Qualifying Offer has not been terminated and continues to be a Qualifying Offer, holders of record (or their duly authorized proxy) of at least ten percent (10%) of the Common Stock then outstanding (excluding Common Stock Beneficially Owned by the offeror and the offeror’s Affiliates and Associates) may submit to the Board, not earlier than ninety (90) Business Days nor later than one hundred twenty (120) Business Days following the commencement of such Qualifying Offer within the meaning of Rule 14d-2(a) under the Exchange Act, a written demand complying with the terms of this Section 23(c) (the “ Special Meeting Demand ”) directing the Board to submit to a vote of stockholders at a special meeting of the stockholders of the Company (a “ Special Meeting ”) a resolution authorizing the exemption of such Qualifying Offer from the provisions of this Agreement (the “ Qualifying Offer Resolution ”).

(ii) A Special Meeting Demand shall be delivered to the Secretary of the Company at the principal executive offices of the Company and must set forth as to the stockholders of record executing the request (x) the names and addresses of such stockholders, as they appear on the Company’s books and records, (y) the number of shares of Common Stock which are owned of record by each of such stockholders, and (z) in the case of any shares of Common Stock that are Beneficially Owned by another Person, an executed certification by the holder of record that such holder has executed such Special Meeting Demand only after obtaining instructions to do so from such Beneficial Owner and attaching evidence thereof. For purposes of a Special Meeting Demand, the record date for determining holders of record eligible to make a Special Meeting Demand shall be the ninetieth (90th) Business Day following commencement, within the meaning of Rule 14d-2(a) under the Exchange Act, of a Qualifying Offer.

(iii) In the event that the Board receives a Special Meeting Demand complying with the provisions of this Section 23(c), the Board shall take such actions as are necessary or desirable to cause the Qualifying Offer Resolution to be submitted to a vote of stockholders at a Special Meeting by including a proposal relating to the adoption of the Qualifying Offer Resolution in the proxy materials of the Company for the Special Meeting. Such Special Meeting shall be convened within ninety (90) Business Days following the Special Meeting Demand (the “ Special Meeting Period ”); provided , however , that if the Company at any time during the Special Meeting Period and prior to a vote on the Qualifying Offer Resolution enters into a Definitive Acquisition Agreement conditioned on the approval by holders of a majority of the outstanding Common Stock,

the Special Meeting Period may be extended by the Board (and any Special Meeting called in connection therewith may be cancelled) if the Qualifying Offer Resolution will be separately submitted to a vote at the same meeting as the Definitive Acquisition Agreement.

(iv) The Board shall set a date for determining the stockholders of record that are entitled to notice of and to vote at the Special Meeting in accordance with the Company’s certificate of incorporation, bylaws and applicable law.

(v) Subject to the requirements of applicable law, the Board may take a position in favor of or opposed to the adoption of the Qualifying Offer Resolution, or no position with respect to the Qualifying Offer Resolution, as it determines to be appropriate in the exercise of its duties. Notwithstanding anything to the contrary contained in this Agreement, if the Board determines that it is in the best interests of the stockholders of the Company to seek an alternative transaction so as to obtain greater value for such stockholders than is being provided by any Qualifying Offer, then the Company shall be entitled to include information relating to such alternative transaction in the proxy soliciting material(s) prepared by the Company in connection with the Special Meeting.

(vi) In the event that the Qualifying Offer continues to be a Qualifying Offer and either (A) the Special Meeting is not convened on or prior to the last day of the Special Meeting Period (the “ Outside Meeting Date ”), or (B) if, at the Special Meeting at which a quorum is present, a majority of the outstanding Common Stock entitled to vote as of the record date for the Special Meeting selected by the Board, not giving effect to any affirmative votes cast by the offeror or any of its Affiliates or Associates, shall vote in favor of the Qualifying Offer Resolution, then the Qualifying Offer shall be deemed exempt from the application of this Agreement to such Qualifying Offer so long as it remains a Qualifying Offer, such exemption to be effective on the Close of Business on the tenth (10th) Business Day after either (y) the Outside Meeting Date or (z) the date on which the results of the vote on the Qualifying Offer Resolution at the Special Meeting are certified as official by the appointed inspectors of election for the Special Meeting, as the case may be (the “ Exemption Date ”).

(vii) Immediately upon the Close of Business on the Exemption Date, if any, without any further action and without any notice, the right to exercise the Rights with respect to the Qualifying Offer will terminate, and notwithstanding anything in this Agreement to the contrary, the consummation of the Qualifying Offer shall not cause the offeror (or its Affiliates or Associates) to become an Acquiring Person.

(viii) The Company shall promptly notify the Rights Agent in writing upon the occurrence of the Exemption Date and, if such notification is given orally, the Company shall confirm the same in writing on or prior to the next Business Day. Until such notice is received by the Rights Agent, the Rights Agent may presume conclusively for all purposes that the Exemption Date has not occurred.

(ix) Notwithstanding anything herein to the contrary, no action or vote by stockholders not in compliance with the provisions of this Section 23(c) shall serve to exempt any offer from the terms of this Agreement.

(x) Nothing in this Section 23(c) shall be construed as limiting or prohibiting the Company or any offeror from proposing or engaging in any acquisition, disposition or other transfer of any securities of the Company, any merger or consolidation involving the Company, any sale or other transfer of assets of the Company, any liquidation, dissolution or winding-up of the Company, or any other business combination or other transaction, or any other action by the Company or such offeror; provided , however , that the holders of the Rights shall have the rights set forth in this Agreement with respect to any such acquisition, disposition, transfer, merger, consolidation, sale, liquidation, dissolution, winding-up, business combination, transaction or action.”

11.        Except as expressly set forth in this Amendment, all other terms of the Rights Agreement shall remain in full force and effect. The term “Agreement” as used in the Rights Agreement shall be deemed to refer to the Rights Agreement as amended hereby.

12.        This Amendment shall be deemed effective as of the date first written above. The Authorized Officer of the Company executing this Amendment hereby certifies to the Rights Agent that the amendments to the Rights Agreement set forth in this Amendment are in compliance with Section 27 of the Rights Agreement and the certification contained in this Section 12 shall constitute the certification required by Section 27 of the Rights Agreement.

13.        This Amendment shall be governed by and construed in accordance with the laws of the State of Delaware applicable to contracts made and to be performed entirely within such State.

14.        This Amendment may be executed in one or more counterparts, and by the different parties hereto in separate counterparts, each of which when executed shall be deemed to be an original, but all of which taken together shall constitute one and the same instrument. A signature to this Amendment executed and/or transmitted electronically shall have the same authority, effect and enforceability as an original signature.

15.        The Rights Agent and the Company hereby waive any notice requirement with respect to each other under the Rights Agreement, if any, pertaining to the matters covered by this Amendment.

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IN WITNESS WHEREOF, the parties hereto have caused this Amendment to be duly executed, all as of the date first above written.