Exhibit 4.2.4

AMENDMENT NO. 2 TO RIGHTS AGREEMENT

This AMENDMENT NO. 2 TO RIGHTS AGREEMENT (this “ Amendment ”) is made as of May 18, 2012 by and between MoSys, Inc., a Delaware corporation (the “ Company ”), and Wells Fargo Bank, N.A. (the “ Rights Agent ”).

WHEREAS, the Company and the Rights Agent are parties to the Rights Agreement dated November 8, 2010, as amended by Amendment No. 1 to Rights Agreement dated July 22, 2011 (as amended, the “ Rights Agreement ”).  All capitalized terms used but not defined herein shall have the meanings assigned to them in the Rights Agreement.

WHEREAS, the Company previously entered into a Voting Agreement, dated July 22, 2011, with certain stockholders of the Company (the “ Stockholders ”) pursuant to which the Company agreed, among other things, to amend the Rights Agreement in order to raise the beneficial ownership limitations applicable to the Stockholders thereunder to 20% and to maintain such amendment in effect as long as the Voting Agreement remained in effect, on the terms and subject to the conditions set forth therein.

WHEREAS, the Company and the Stockholders have terminated the Voting Agreement, effective as of the date hereof.

WHEREAS, in connection with the termination of the Voting Agreement, the Company and the Rights Agent desire to amend the Rights Agreement as provided herein.

NOW, THEREFORE, for good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the parties hereby agree as follows:

1.             The definition of “Acquiring Person” in Section 1 of the Rights Agreement is hereby amended and restated in its entirety to read as follows:

“ Acquiring Person’’ shall mean any Person (as such term is hereinafter defined) who or which, together with all Affiliates and Associates (as such terms are hereinafter defined) of such Person, shall be the Beneficial Owner (as such term is hereinafter defined) of 15%, or in the case of a Grandfathered Stockholder, 20%, or more of the Common Shares then outstanding, but shall not include the Company, any Subsidiary (as such term is hereinafter defined) of the Company, any employee benefit plan of the Company or of any Subsidiary of the Company, or of any entity holding Common Shares for or pursuant to the terms of any such employee benefit plan.  Notwithstanding the foregoing, (1) no Person shall become an “Acquiring Person” as the result of an acquisition of Common Shares by the Company which, by reducing the number of shares outstanding, increases the proportionate number of shares beneficially owned by such Person to 15% (or in the case of a Grandfathered Stockholder, 20%) or more of the Common Shares of the Company then outstanding; provided , however , that if a Person shall become the Beneficial Owner of 15% (or in the case of a Grandfathered Stockholder, 20%) or more of the Common Shares then outstanding by reason of share purchases by the Company and shall, after such share purchases by the Company, become the Beneficial Owner of any additional Common Shares, then such Person shall be deemed to be an “Acquiring Person”; and (2) if the Board of Directors of the Company determines in good faith that a Person who would otherwise be an “Acquiring

Person,” as defined pursuant to the foregoing provisions of this paragraph, has become such inadvertently, and such Person divests as promptly as practicable a sufficient number of Common Shares so that such Person would no longer be an “Acquiring Person,” as defined pursuant to the foregoing provisions of this paragraph, then such Person shall not be deemed to have become an “Acquiring Person” for any purposes of this Agreement.

Notwithstanding anything in this Agreement that might otherwise be deemed to the contrary, none of the I&S Parties, individually or collectively, shall be deemed to be an Acquiring Person as long as none of the Common Shares held by any of the I&S Parties are acquired or held with a purpose or effect of changing or influencing control of the Company, or in connection with or as a participant in any transaction having that purpose or effect, as determined in the sole discretion of the Board of Directors of the Company.  This exclusion is limited to Common Shares as to which I&S parties share dispositive power but have only limited voting power of the type described in SEC Rule 13d-3(d)(2).  Any single account holder or retail customer of I&S, and any single broker at I&S with respect to such broker’s personal trading account, shall remain subject to the 15% limitation on Beneficial Ownership contained in this Section 1(a).  For purposes of this paragraph shares of Common Stock as to which an I&S Party has, or I&S Parties have, dispositive power and only non-discretionary voting power (as defined in SEC Rule 13d-3(d)(2)), with no “direct pecuniary interest” or “indirect pecuniary interest” (as defined under SEC Rule 16a-1(a)) therein, shall be excluded from the calculation of Beneficial Ownership under Section 1(a).

2.             Section 1 of the Rights Agreement is further amended by striking the defined term “ Artis ” therefrom.

3.             Section 3(a) of the Rights Agreement is amended and restated in its entirety to read as follows:

(a)           Until the earlier of the close of business on (i) the tenth day after the Shares Acquisition Date, or (ii) the tenth Business Day (or such later date as may be determined by action of the Board of Directors prior to such time as any Person becomes an Acquiring Person) after the date of the commencement by any Person (other than the Company, any Subsidiary of the Company, any employee benefit plan of the Company or of any Subsidiary of the Company or any entity holding Common Shares for or pursuant to the terms of any such plan) of, or of the first public announcement of the intention of any Person (other than any of the persons referred to in the preceding sentence) or of any Subsidiary of the Company or any entity holding Common Shares for or pursuant to the terms of any such plan) to commence, a tender or exchange offer the consummation of which would result in any Person becoming the Beneficial Owner of Common Shares aggregating 15%, or in the case of a Grandfathered Stockholder, 20%, or more of the then outstanding Common Shares (irrespective of whether any Common Shares are actually purchased pursuant to such offer) (including any such date which is after the date of this Agreement and prior to the issuance of the Rights), (the earliest of such dates being herein referred to as the “Distribution Date” ), (x) the Rights will be evidenced (subject to the provisions of Section 3(b) hereof) by the certificates for Common Shares registered in the names of the holders thereof (which certificates shall also be deemed to be Right Certificates), or by Book Entry Common Shares, and not by separate Right Certificates, and (y) the right to receive Right Certificates will be

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transferable only in connection with the transfer of Common Shares. As soon as practicable after the Distribution Date, the Company will prepare and execute, the Rights Agent will countersign, and the Company will send or cause to be sent (and the Rights Agent will, if requested, send) by first-class, insured, postage-prepaid mail, to each record holder of Common Shares as of the close of business on the Distribution Date, at the address of such holder shown on the records of the Company, a Right Certificate, in substantially the form of Exhibit A hereto (a “ Right Certificate ”), evidencing one Right for each Common Share so held. As of the Distribution Date, the Rights will be evidenced solely by such Right Certificates.

4.             The form of Right Certificate and Summary of Rights are hereby amended consistently with the terms of this Amendment and as distributed by the Company shall be revised to reflect such terms, if then applicable.

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

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