Exhibit 10.3

[ * ] = Certain confidential information contained in this document, marked by brackets, has been omitted and filed separately with the Securities and Exchange Commission pursuant to Rule 24b-2 of the Securities Exchange Act of 1934, as amended.

AMENDMENT NO. 2 TO THE COLLABORATION AGREEMENT

BETWEEN

EXELIXIS, INC., AND BRISTOL-MYERS SQUIBB COMPANY

THIS AMENDMENT NO. 2 (“Amendment No. 2”) to the Agreement (defined below) is effective as of October 1, 2009 (the “Amendment No. 2 Effective Date”) by and between Exelixis, Inc., a Delaware corporation having an address at 170 Harbor Way, P.O. Box 511, South San Francisco, California 94083-0511 (“Exelixis”) and Bristol-Myers Squibb Company, a Delaware corporation having an address at 345 Park Avenue, New York, New York 10154 (“BMS”). Exelixis and BMS may be referred to individually as a “Party” and collectively as the “Parties”.

WHEREAS, Exelixis and BMS entered into that certain Collaboration Agreement executed as of December 15, 2006, and as amended to be effective on January 11, 2007 (the Collaboration Agreement, as amended, the “Agreement”), for the purposes of applying Exelixis’ technology and expertise to the discovery, lead optimization and characterization of small molecule compounds that directly bind and modulate certain oncology targets, with a goal of filing Investigational New Drug applications for such small molecule compounds, and to provide for the development and commercialization of novel therapeutic and prophylactic products based on such compounds; and

WHEREAS, the Parties desire to amend the Agreement to clarify the exclusivity of antagonists of the target known as [ * ] ([ * ]), as set forth below.

NOW, THEREFORE, in consideration of the premises and mutual covenants herein contained, and for other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the Parties hereto agree as follows:

1. AMENDMENT OF THE AGREEMENT

The Parties hereby agree to amend the terms of the Agreement as provided below, effective as of the Amendment No. 2 Effective Date. To the extent that the Agreement is explicitly amended by this Amendment No. 2, the terms of this Amendment No. 2 will control where the terms of the Agreement are contrary to or conflict with the following provision. Where the Agreement is not explicitly amended, the terms of the Agreement will remain in full force and effect. Capitalized terms used in this Amendment No. 2 that are not otherwise defined herein shall have the same meanings as such terms have in the Agreement.

1.1 Amendment of Section 8.6. The Parties agree to add a new Section 8.6(i) of the Agreement as follows:

“8.6(j) [ * ] for [ * ] ([ * ]) Agonists. Notwithstanding anything to the contrary set forth in this Article 8, [ * ] Party shall be permitted to engage in research, development or commercialization of products that directly bind and agonize the [ * ] known as [ * ] and that are outside the scope of this Agreement (i.e., such products [ * ] Collaboration Compounds or

Products under this Agreement); provided, however that a compound shall be deemed to agonize [ * ] only if such compound has an efficacy of [ * ] percent ([ * ]%) or greater when compared to [ * ] ([ * ]) in the [ * ] assay.”

2. MISCELLANEOUS

2.1 Full Force and Effect. This Amendment No. 2 amends the terms of the Agreement and is deemed incorporated into, and governed by all other terms of, the Agreement. The provisions of the Agreement, as amended by this Amendment No. 2, remain in full force and effect.

2.2 Further Actions. Each Party shall execute, acknowledge and deliver such further instruments, and do all other acts, as may be necessary or appropriate in order to carry out the purposes and intent of this Amendment No. 2.

2.3 Counterparts. This Amendment No. 2 may be signed in counterparts, each and every one of which shall be deemed an original, notwithstanding variations in format or file designation, which may result from the electronic transmission, storage and printing of copies of this Amendment No. 2 from separate computers or printers. Facsimile signatures shall be treated as original signatures.

Signature page follows

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[ * ] = Certain confidential information contained in this document, marked by brackets, has been omitted and filed separately with the Securities and Exchange Commission pursuant to Rule 24b-2 of the Securities Exchange Act of 1934, as amended.

IN WITNESS WHEREOF, the Parties have caused this Amendment No. 2 to be executed by their duly authorized representatives as of the Amendment No. 2 Effective Date. The date that this Amendment No. 2 is signed shall not be construed to imply that the document was made effective on that date.

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[ * ] = Certain confidential information contained in this document, marked by brackets, has been omitted and filed separately with the Securities and Exchange Commission pursuant to Rule 24b-2 of the Securities Exchange Act of 1934, as amended.