Exhibit 10.13

FIRST AMENDMENT TO

STOCKHOLDERS AGREEMENT

This FIRST AMENDMENT (this “First Amendment”) TO THE STOCKHOLDERS AGREEMENT dated as of November 17, 2011 (the “Agreement”) by and among Plains Offshore Operations Inc., a Delaware corporation (the “Company”), PXP Resources LLC, a Delaware limited liability company, Plains Exploration & Production Company, a Delaware corporation (“PXP”), PXP Resources LLC, a Delaware limited liability company (“PXP Resources”) and each investor named in Schedule A thereto (collectively, the “Investors”) is made and entered into as of December 22, 2011 by and between the Company, PXP, PXP Resources and the Investors.

WHEREAS, the Company, PXP, PXP Resources and the Investors desire to amend the Agreement.

NOW, THEREFORE, in consideration of the foregoing recitals and the agreements contained herein, and for other good and valuable consideration, the receipt and sufficiency of which are hereby expressly acknowledged, the parties hereto, intending to be legally bound, do hereby agree as follows:

If the Company agrees to acquire additional Deepwater GOM Assets prior to an Initial Public Offering under this Section 2.02(c), then each of the holders of Common Stock, Class A Common Stock and Class B Common Stock (the “Common Stockholders”) and Preferred Stockholders shall contribute its proportionate share (determined on an as-converted basis) of any capital necessary to fund such acquisition through the purchase from the Company of additional shares of Class A Common Stock at a price of $20.00 per share; provided, however, that notwithstanding anything to the contrary in Section 3.08, any or all of MTP Energy Master Fund Ltd., MTP Energy Opportunities Fund I LLC, MTP Opportunity Fund, LLC, Triangle Peak Partners Private Equity, LP and Hipparchus Fund LP (each, together with its Affiliates, a “Magnetar Fund”, and collectively, “Magnetar”), may assign, in whole or in part (including without limitation an assignment limited to a particular offer under this Section 2.02(c)), its rights and (to the extent related to such assigned rights) obligations under this Section 2.02(c), in their capacity as holders of Preferred Stock, to acquire additional shares of Class A Common Stock to one or more of Energy Fund XV, L.P., Energy Fund XV-A, L.P., Energy Fund XV-B, L.P. and Energy XV Blocker (Plains), LLC (each, together with its Affiliates,

an “EIG Fund” and collectively “EIG”), subject to the assignee EIG Fund assuming such assigned obligations under this Section 2.02(c) and notifying the Company of such assignment and assumption (and specifying the rights and obligations assigned and assumed) and (1) to the extent an EIG Fund assumes such obligations under this Section 2.02(c), the Magnetar Fund assigning such obligations under this Section 2.02(c) shall be relieved of such rights and obligations under this Section 2.02(c) and (2) the rights and obligations so assigned and assumed shall be deemed to be the rights and obligations of the EIG Fund that has assumed such obligations; provided further, however, that if any holder of Common Stock, Class A Common Stock or Class B Common Stock fails to purchase such additional shares of Class A Common Stock, then PXP shall acquire such additional shares of Class A Common Stock.

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IN WITNESS WHEREOF, the Parties hereto have entered into this First Amendment as of the date first written above.

[Signature Page to First Amendment to Stockholders Agreement]

[Signature Page to First Amendment to Stockholders Agreement]

[Signature Page to First Amendment to Stockholders Agreement]