Exhibit 10.4

VERACYTE, INC.

6000 Shoreline Court, Suite 300

South San Francisco, CA 94080

STRICTLY CONFIDENTIAL

March 30, 2016

Visium Healthcare Partners, LP

888 7th Avenue, 22nd Floor

New York, NY 10019

Re:                             Agreement Regarding Potential Opportunity to Purchase Common Equity Interests

Ladies and Gentleman:

Reference is made to the Credit Agreement (as amended, restated, supplemented or otherwise modified, the “Credit Agreement”), dated as of March 25, 2016 by and among Veracyte, Inc., a Delaware corporation (the “Company”), as Borrower under the Credit Agreement, each of the Guarantors party to the Credit Agreement, Visium Healthcare Partners, LP, a Delaware limited partnership, as Administrative Agent under the Credit Agreement, and each of the Lenders party to the Credit Agreement, including their successors and assigns (the “Purchasers”).

In connection with entering into the Credit Agreement, the Company, the Administrative Agent, and each of the Purchasers desire to enter into this letter agreement (this “Letter Agreement”) with respect to the potential opportunity to purchase Common Equity (as defined below) of the Company by the Purchasers in connection with one or more Equity Offerings (as defined below) for a period of one year following the Funding Date, subject to the terms and conditions of this Letter Agreement.  As used in this Letter Agreement, “Common Equity” means (i) shares of common stock of the Company, (ii) warrants, options or other rights for the purchase or acquisition from the Company of shares of common stock of the Company or (iii) securities convertible into or exchangeable for shares of common stock of the Company.

Each of the parties to this Letter Agreement agree that this Letter Agreement is effective as of the Funding Date. Unless otherwise defined herein, capitalized terms used in this Letter Agreement shall have the meanings set forth in the Credit Agreement.

In consideration of the foregoing and the mutual promises, representations, warranties, and covenants hereinafter set forth and for other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the parties hereto agree as follows:

1.                                      Participation Rights.

(a)                                 In the event the Company intends to offer Common Equity pursuant to one or more Qualifying Follow-On Offerings (as defined below) no later than one year following the Funding Date, each Purchaser, in its sole discretion, shall have the right but not the obligation to submit to the underwriters a non-binding indication of interest to purchase in each Qualifying Follow-On Offering (the “Public Offering Participation Right”) such Purchaser’s Pro Rata Percentage (as defined below) of up to an aggregate number of shares or units of Common Equity equal to (i) the Available Amount (as defined below) divided by (ii) the price at which each share or unit of Common Equity is issued and sold to the public in the Qualifying Follow-On Offering (the “Public Offering Price”), at a price per share or unit equal to the Public Offering Price in the closing of the Qualifying Follow-On Offering (the “Public Offering Closing”). Notwithstanding the foregoing, the Public Offering Participation Right shall be subject to (i) a determination by any of the Company, the Administrative Agent (on behalf of the Purchasers) or the underwriters, with the advice of outside counsel, that the Public Offering

Participation Right does not violate applicable Laws and the rules, regulations and requirements of securities exchanges or securities listing organizations, including but not limited to any applicable state or federal securities laws or regulations and any applicable rule, policy or limit imposed by the U.S. Securities and Exchange Commission, the National Association of Securities Dealers, or any securities exchange (“Applicable Law”) and (ii) any carve backs, restrictions and other limitations reasonably requested by the Company’s underwriters in connection with the Qualifying Follow-On Offering.  For purposes of this Letter Agreement, “Available Amount”, as determined from time to time, means (i) Five Million Dollars ($5,000,000) less (ii) the aggregate dollar amount paid by the Purchasers, if any, to purchase Common Equity in Equity Offerings prior to when the Available Amount is being calculated.

(b)                                 Notwithstanding the foregoing, in the event (i) any of the Company, the Administrative Agent (on behalf of the Purchasers), or the underwriters, with the advice of counsel, determine that the Public Offering Participation Right violates Applicable Laws (including, without limitation, as a result of the Purchasers having material non-public information), (ii) the Public Offering Participation Right is limited by carve backs, restrictions or other limitations reasonably requested by the underwriters, or (iii) the Purchasers are otherwise not permitted or decline, in their sole discretion, to participate in a Qualifying Follow-On Offering pursuant to the terms hereof (each, a “Public Offering Disqualification Event”), then, each Purchaser, in its sole discretion, shall have the right but not the obligation (the “Private Placement Participation Right”), to purchase, in a private placement exempt from the registration requirements of the Securities Act of 1933, as amended, concurrent to the Qualifying Follow-On Offering, (the “Private Placement”), such Purchaser’s Pro Rata Percentage (as defined below) of up to an aggregate number of shares or units of Common Equity equal to (A) the Available Amount divided by (B) the Equity Purchase Price (as defined below), at a price per share or unit equal to the Equity Purchase Price (the “Private Placement Price”) in a closing to be held concurrently with the closing of the Qualifying Follow-On Offering. Notwithstanding the foregoing, the Participation Right shall be subject to a determination by the Company or the Administrative Agent with the advice of outside counsel, that the Private Placement does not violate Applicable Law.If neither the Public Offering Participation Right nor the Private Placement Participation Right with respect to a Qualifying Follow-On Offering can be effected in compliance with Applicable Law, then the Company shall have no further obligation to the Purchasers pursuant to this Letter Agreement with respect to such Qualifying Follow-On Offering.

(c)                                  In the event the Company intends to offer or sell Common Equity in one or more transactions in any manner other than pursuant to a Qualifying Follow-On Offering or Private Placement as set forth above, including without limitation, any other private placement of Common Equity solely for cash, but excluding an underwritten Rule 144A offering of securities convertible into or exchangeable for shares of common stock of the Company (a “Private Sale”, and together with a Private Placement and a Qualifying Follow-On Offering, each, an “Equity Offering”), no later than one year following the Funding Date, then, each Purchaser, in its sole discretion, shall have the right but not the obligation (the “Private Sale Participation Right”), to participate in such Private Sale and purchase such Purchaser’s Pro Rata Percentage of up to an aggregate number of shares or units of Common Equity equal to (i) the Available Amount divided by (ii) the Equity Purchase Price, at a price per share or unit equal to the Equity Purchase Price. Notwithstanding the foregoing, the following shall not be deemed to be Private Sales or offers or sales of Common Equity:  (i) issuances of equity compensation to employees and directors of the Company pursuant to the equity compensation plans that have been approved by shareholders of the Company prior to the Funding Date and (ii) issuances of Common Equity in connection with strategic transactions involving the Company and other entities, including joint ventures, manufacturing, marketing or distribution arrangements, and technology transfer or development arrangements.

(d)                                 For purposes of this Letter Agreement, a “Qualifying Follow-On Offering” means the issuance by the Company of Common Equity in an underwritten primary public offering (other than a public offering pursuant to a registration statement on Form S-8) pursuant to an effective registration statement filed with the SEC in accordance with the Securities Act of 1933, as amended, and such Equity Interests are listed on a nationally-recognized stock exchange in the United States.  For purposes of clarity, sales of Common Equity pursuant to the Company’s existing Controlled Equity Offering Sales Agreement shall not constitute a Qualifying Follow-On Offering.  The “Purchaser’s Pro Rata Percentage” means, with respect to each Purchaser at the time of the Closing, the percentage of the Outstanding Amount of all Loans and Commitments under the Credit Agreement represented by the Outstanding Amount of the Purchaser’s Loans and Commitments at the time of the Closing.  The “Equity Purchase Price” means (i) in the case of a Qualifying Follow-On Offering or Private Placement, the Public

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Offering Price and (ii) in the case of a Private Sale, the price per share or unit negotiated in good faith by the Purchasers, any other purchasers of Common Equity in such Private Sale, and the Company; provided, however, in no event will the Equity Purchase Price be greater than the purchase price offered to a third-party purchaser in the applicable Equity Offering.

(e)                                  In the event of a Qualifying Follow-On Offering, at least fifteen (15) business days prior to the anticipated effective date of the registration statement for the Qualifying Follow-On Offering or, if the Qualifying Follow-On Offering is to be effected using an existing effective shelf registration statement (a “Shelf Takedown”), at least twelve (12) business days prior to the anticipated initial public marketing date for the Shelf Takedown, the Company shall deliver to the Purchasers written notice (the “Qualifying Follow-On Offering Notice”) specifying (i) that the Company has filed a registration statement for a Qualifying Follow-On Offering or, in the case of a Shelf Takedown, the Company anticipates effecting such Shelf Takedown, (ii) the anticipated effective date of the registration statement or initial public marketing date, as the case may be, for the Qualifying Follow-On Offering, and (iii) any other appropriate information required by Applicable Law.  In the case of a Private Sale, at least twelve (12) business days prior to the anticipated closing of any Private Sale, the Company shall deliver to the Purchasers a written notice (the “Private Sale Offering Notice”) specifying that the Company intends to offer Common Equity for sale and the anticipated closing date of the sale of such Common Equity that includes copies of the definitive documentation pursuant to which the Company intends to offer or sell the Common Equity as well as any other appropriate information required by Applicable Law.

(f)                                   Upon receipt of the Qualifying Follow-On Offering Notice or Private Sale Offering Notice, as applicable, each Purchaser shall promptly, but in no event later than twelve (12) business days (eight (8) business days in the case of a Shelf Takedown) from receipt of such notice in the case of a Qualifying Follow-On Offering or ten (10) business days from receipt of such notice in the case of a Private Sale, inform the Company in writing whether such Purchaser wishes to exercise its (i) Public Offering Participation Right,or (ii) Private Placement Participation Right or (iii) Private Sale Participation Right.

(g)                                 As a condition to each Purchaser participating in the Qualifying Follow-On Offering, each such Purchaser shall execute such other documents as may be required of all participants in the Qualifying Follow-On Offering or as deemed reasonably necessary by the underwriter of the Qualifying Follow-On Offering or the Company, as applicable, including, without limitation a “lock-up” agreement; provided, however, that no Purchaser will be required to enter into a lock-up agreement unless all directors, executive officers and significant shareholders of the Company enter into a significantly similar lock-up agreement.

(h)                                 As a condition to each Purchaser participating in a Private Placement or Private Sale, as applicable, each such Purchaser shall execute such other documents as may be deemed reasonably necessary by the Company, including, without limitation a “lock-up” agreement; provided, however, that no Purchaser will be required to enter into a lock-up agreement unless, it is for ninety (90) days or less and all directors, executive officers and significant shareholders of the Company enter into a significantly similar lock-up agreements.

2.                                      Undertakings in Connection with Exercise of Private Placement Participation Right

In the event a Purchaser exercises its Private Placement Participation Right, the Company and the Purchasers shall, on or before the date of the final prospectus relating to the registration by the Company of shares or units of Common Equity in the Qualifying Follow-On Offering (the “Final Prospectus Date”), execute and deliver such other documents, including a stock purchase agreement containing representations, warranties and conditions to closing, that, in each case, are customary for a transaction structured as a concurrent private placement with a follow-on public offering, that are reasonably satisfactory to the Company and each Purchaser.

3.                                      Undertakings in Connection with Exercise of Private Sale Participation Right

In the event a Purchaser exercises its Private Sale Participation Right, the Company and the Purchasers shall, on or before the closing date of the Private Sale (the “Private Sale Closing Date”), execute and deliver the definitive documents, pursuant to which the Company is selling or issuing the Common Equity, including a stock purchase agreement containing representations, warranties and conditions to closing, that, in each case, are customary for a transaction structured as a similar private sale, that are reasonably satisfactory to the

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Company and each Purchaser.  The terms included in any definitive documentation between the Company and Purchaser governing a Private Sale shall be no less favorable than those given to other purchasers of Common Equity in the Private Sale.

4.                                      Termination.  The covenants, rights and obligations set forth in Sections 1, 2 and 3 of this Letter Agreement shall terminate and be of no further force or effect upon the earliest to occur of (i) the Available Amount being zero (0) due to purchases by the Purchasers of Five Million Dollars ($5,000,000) of Common Equity, or (ii) the date that is one (1) year from the Funding Date.

5.                                      Successors and Assigns.  The provisions of this Letter Agreement shall be binding upon and inure to the benefit of the parties hereto and their respective successors and assigns permitted hereby, provided that (i) the Company may not assign or otherwise transfer any of its rights or obligations hereunder without the prior written consent of each Purchaser, and, (ii) except as otherwise permitted herein, each Purchaser may not assign or otherwise transfer any of its rights or obligations hereunder without the prior written consent of the Company. Notwithstanding anything to the contrary herein, each Purchaser shall assign without consent of the Company (but with notice to the Company) a proportionate part of its rights and obligations under this Letter Agreement to any successor or assign of such Purchaser’s rights and obligations under the Credit Agreement, subject to compliance with Applicable Law, including federal and state securities laws (a “Required Assignment”). Each Required Assignment hereunder shall be proportionate and ratable to its corresponding assignment under the Credit Agreement in accordance with Section 11.06(b)(ii) of the Credit Agreement.  Notwithstanding anything to the contrary herein, each Purchaser shall be permitted to assign or transfer any of its rights or obligations hereunder to any Affiliate of such Purchaser without the consent of the Company.

6.                                      Miscellaneous.

(a)                                 Governing Law. This Letter Agreement and any controversy arising out of or relating to this Letter Agreement shall be governed by and construed under the laws of the State of New York, without regard to conflict of law principles that would result in the application of any laws other than the laws of the State of New York.

(b)                                 [Reserved]

(c)                                  Entire Agreement. This Letter Agreement and the exhibits and schedules hereto, constitute the full and entire understanding and agreement between the parties with regard to the subjects hereof and no party shall be liable for or bound to any other in any manner by any oral or written representations, warranties, covenants and agreements except as specifically set forth herein.

(d)                                 Severability. In the event one or more of the provisions of this Letter Agreement should, for any reason, be held to be invalid, illegal or unenforceable in any respect, such invalidity, illegality or unenforceability shall not affect any other provisions of this Letter Agreement, and this Letter Agreement shall be construed as if such invalid, illegal or unenforceable provision had never been contained herein.

(e)                                  Amendment and Waiver. This Letter Agreement may be amended or modified, and the rights and the obligations of the Company and the rights and obligations of the Purchasers may be waived, only upon the written consent of the Company and each Purchaser.

(f)                                   Delays or Omissions. It is agreed that no delay or omission to exercise any right, power or remedy accruing to any party, upon any breach, default or noncompliance by another party under this Letter Agreement, shall impair any such right, power or remedy, nor shall it be construed to be a waiver of any such breach, default or noncompliance, or any acquiescence therein, or waiver of or acquiescence in any similar breach, default or noncompliance thereafter occurring. It is further agreed that any waiver, permit, consent or approval of any kind or character on any party’s part of any breach, default or noncompliance under this Letter Agreement or any waiver on such party’s part of any provisions or conditions of this Letter Agreement must be in writing and shall be effective only to the extent specifically set forth in such writing. All remedies, either under this Letter Agreement

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the organizational documents of the Company, the Credit Agreement or otherwise afforded to any party, shall be cumulative and not alternative.

(g)                                 Notices. All notices required or permitted hereunder shall be in writing and shall be deemed effectively given when delivered in compliance with Section 11.02 of the Credit Agreement.

(h)                                 Expenses. The Company shall pay all out-of-pocket expenses incurred by the Administrative Agent and its Affiliates (including the fees, charges and disbursements of counsel for the Administrative Agent), in connection with the preparation, negotiation, execution, and delivery of this Letter Agreement.  Each of the Company, on the one hand, and the Administrative Agent and its Affiliates, on the other hand, shall bear their own expenses in connection with the administration of this Letter Agreement or any amendments, modifications or waivers of the provisions hereof (whether or not the transactions contemplated hereby shall be consummated).

(i)                                    Titles and Subtitles. The titles of the sections and subsections of this Letter Agreement are for convenience of reference only and are not to be considered in construing this Letter Agreement.

(j)                                    Counterparts. This Letter Agreement may be executed in any number of counterparts, each of which shall be an original, but all of which together shall constitute one instrument. Any or all parties may execute this Letter Agreement by facsimile signature or scanned signature in PDF format and any such facsimile signature or scanned signature, if identified, legible and complete, shall be deemed an original signature and each of the parties is hereby authorized to rely thereon.

(k)                                 Broker’s Fees. Each party hereto represents and warrants that no agent, broker, investment banker, person or firm acting on behalf of or under the authority of such party hereto is or will be entitled to any broker’s or finder’s fee or any other commission directly or indirectly in connection with the transactions contemplated herein. Each party hereto further agrees to indemnify each other party for any claims, losses or expenses incurred by such other party as a result of the representation in this Section 6(k) being untrue.

(l)                                    Pronouns. All pronouns contained herein, and any variations thereof, shall be deemed to refer to the masculine, feminine or neutral, singular or plural, as to the identity of the parties hereto may require.

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If you are in agreement with the terms set forth above, please sign the Letter Agreement in the space provided below:

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