Sponsor Support Agreement, dated as of March 17, 2022, by and among Brookline Capital Acquisition Corp., Apexigen, Inc. and Brookline Capital Holdings, LLC

Exhibit 10.3

SPONSOR SUPPORT AGREEMENT

This SPONSOR SUPPORT AGREEMENT (this “Agreement”), dated as of March 17, 2022, is entered into by and among Brookline Capital Holdings, LLC, a Delaware limited liability company (the “Sponsor”), Brookline Capital Acquisition Corp., a Delaware corporation (“BCAC”), and Apexigen, Inc., a Delaware corporation (the “Company”).

RECITALS

WHEREAS, concurrently herewith, the Company, Project Barolo Merger Sub, LLC, a Delaware limited liability company (“Merger Sub”), and BCAC are entering into a Business Combination Agreement (as amended, supplemented, restated or otherwise modified from time to time, the “BCA”), pursuant to which (and subject to the terms and conditions set forth therein) Merger Sub will merge with and into the Company (the “Merger”), with the Company surviving the Merger as a wholly owned subsidiary of BCAC;

WHEREAS, capitalized terms used but not otherwise defined in this Agreement shall have the meanings ascribed to them in the BCA; and

WHEREAS, as a condition and inducement to the willingness of BCAC and the Company to enter into the BCA, BCAC, the Company and the Sponsor are entering into this Agreement.

AGREEMENT

NOW, THEREFORE, in consideration of the foregoing and the mutual covenants and agreements set forth herein, and for other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, and intending to be legally bound hereby, the Sponsor, BCAC and the Company hereby agree as follows:

1. Voting Agreement. The Sponsor hereby unconditionally and irrevocably agrees that during the period from the date hereof through the Termination Date as determined in accordance with Section 24, at the BCAC Stockholders’ Meeting or at any other meeting of the stockholders of BCAC (whether annual or special and whether or not an adjourned or postponed meeting, however called and including any adjournment or postponement thereof) and in connection with any action by written consent of the stockholders of BCAC requested by the BCAC Board or undertaken as contemplated by the Transactions, the Sponsor shall:

(a) when such meeting is held, appear at such meeting or otherwise cause all shares of BCAC Common Stock or any other voting securities of BCAC which it holds, owns or is entitled to vote, whether as shares or as a constituent part of a unit of securities and whether owned as of the date of or later acquired (the “Sponsor Shares”), to be counted as present thereat for the purpose of establishing a quorum;

(b) vote (or execute and return an action by written consent), or cause to be voted at such meeting (or validly execute and return and cause such consent to be granted with respect to), all of the Sponsor Shares in favor of (i) the approval and adoption of the BCA and approval of the Merger and all other transactions contemplated by the BCA and (ii) against any action, agreement or transaction or proposal that would result in a breach of any covenant, representation or warranty or any other obligation or agreement of BCAC under the BCA or that would reasonably be expected to result in the failure of the Merger from being consummated and (iii) each of the proposals and any other matters necessary or reasonably requested by BCAC for consummation of the Merger and the other transactions contemplated by the BCA; and

(c) vote (or execute and return an action by written consent), or cause to be voted at such meeting (or validly execute and return and cause such consent to be granted with respect to), all of the Sponsor Shares against (i) any Business Combination Proposal other than with the Company and (ii) any other action that would reasonably be expected to (x) materially impede, interfere with, delay, postpone or adversely affect the Merger or any of the other transactions contemplated by the BCA, or (y) result in a breach of any covenant, representation or warranty or other obligation or agreement of the Sponsor contained in this Agreement.

2. Sponsor Promote Adjustment. In connection with the consummation of the Transactions, Sponsor agrees that, subject to the satisfaction or waiver of each of the conditions to Closing set forth in Sections 8.01, 8.02 and 8.03 of the BCA, immediately prior to the Effective Time, in the event the BCAC Related Funds Amount at Closing that are available to the Company are less than $20,000,000, that number of Sponsor Shares (the “Surrendered Shares”) equal to (x) one (1) minus the quotient of the BCAC Related Funds Amount divided by $20,000,000, multiplied by (y) one-third (1/3) of the total number of Sponsor Shares, shall be deemed automatically forfeited and cancelled without any further actions by the Sponsor or any other Person, and such Surrendered Shares will be recorded as cancelled by the Company.

3. Transfer of Shares. Except as otherwise contemplated by the BCA or this Agreement, the Sponsor agrees that prior to the Termination Date it shall not, without the consent of the Company, directly or indirectly, (a) offer for sale, sell, assign, transfer (including by operation of law), create any lien or pledge, dispose of or otherwise encumber any of the Sponsor Shares (any of the forgoing, a “Transfer”) or otherwise agree to do any of the foregoing, (b) deposit any Sponsor Shares into a voting trust or enter into a voting agreement or arrangement or grant any proxy or power of attorney with respect thereto that is inconsistent with this Agreement or (c) enter into any contract, option or other arrangement or undertaking requiring the Transfer of any Sponsor Shares. The Sponsor expressly agrees to continue to comply with the restrictions on transfer of the Sponsor Shares set forth in Section 7 of that certain side letter between the Sponsor and BCAC dated January 28, 2021, and neither the Company nor BCAC shall agree to any waiver, amendment or modification of such provisions without the prior written consent of the Company. Notwithstanding the foregoing, this Section 3 shall also not prohibit a Transfer of Sponsor Shares by Sponsor to an affiliate of Sponsor; provided, that such Transfer shall be permitted only if, prior to or in connection with such Transfer, the transferee agrees in writing, reasonably satisfactory in form and substance to the Company, to assume all of the obligations of Sponsor hereunder and to be bound by the terms of this Agreement.

4. No Solicitation of Transactions. The Sponsor agrees prior to the Termination Date not to directly or indirectly, through any of its affiliates or Representatives, (a) solicit, initiate or knowingly encourage (including by furnishing information) the submission of, or participate in any discussions or negotiations with, any Person (other than the Company or its affiliates or

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Representatives), concerning, relating to or which is intended or is reasonably likely to give rise to or result in, a Business Combination Proposal in respect of BCAC other than with the Company. Sponsor shall, and shall cause its affiliates and Representatives to, immediately cease any and all existing discussions or negotiations with any Person (other than with the Company, its stockholders and their respective affiliates and Representatives) conducted prior to the date hereof with respect to, or which is reasonably likely to give rise to or result in, a Business Combination Proposal in respect of BCAC. If the Sponsor or any of its affiliates or Representatives receives any inquiry or proposal with respect to a Business Combination Proposal in respect of BCAC, then Sponsor shall promptly (and in no event later than twenty-four (24) hours after the Sponsor becomes aware of such inquiry or proposal) notify such Person in writing that BCAC is subject to an exclusivity agreement with respect to the Merger that prohibits Sponsor from considering such inquiry or proposal and, in such event, Sponsor shall also promptly notify the Company of such facts and circumstances (provided that Sponsor shall not be obligated to provide such notice in violation of any obligation of confidentiality owed to any third party or any Law).

5. Representations and Warranties of the Sponsor. The Sponsor hereby represents and warrants to BCAC and the Company as follows:

(a) The Sponsor is the only record and a beneficial owner (within the meaning of Rule 13d-3 under the Exchange Act) of, and has good, valid and marketable title to, the Sponsor Shares (which, as of the date hereof, consists of 1,428,250 shares of BCAC Common Stock), free and clear of Liens other than as created by this Agreement or Sponsor’s organizational documents or the organizational documents of BCAC (including, without limitation, for the purposes hereof, any agreement between or among stockholders of BCAC).

(b) The Sponsor (i) has full voting power, full power of disposition and full power to issue instructions with respect to the matters set forth herein, in each case, with respect to the Sponsor Shares, (ii) has not entered into any voting agreement or voting trust with respect to any of the Sponsor Shares that is inconsistent with the Sponsor’s obligations pursuant to this Agreement, (iii) has not granted a proxy or power of attorney with respect to any of the Sponsor Shares that is inconsistent with the Sponsor’s obligations pursuant to this Agreement and (iv) has not entered into any agreement or undertaking that is otherwise inconsistent with, or would interfere with, or prohibit or prevent it from satisfying, its obligations pursuant to this Agreement.

(c) The Sponsor (i) is a legal entity duly organized, validly existing and, to the extent such concept is applicable, in good standing under the Laws of the jurisdiction of its organization and (ii) has all requisite limited liability company or other power and authority and has taken all limited liability company or other action necessary in order to, execute, deliver and perform its obligations under this Agreement and to consummate the transactions contemplated hereby. This Agreement has been duly executed and delivered by the Sponsor and constitutes a valid and binding agreement of the Sponsor enforceable against the Sponsor in accordance with its terms, subject to applicable bankruptcy, insolvency, fraudulent conveyance, reorganization, moratorium and similar Laws affecting creditors’ rights generally and subject, as to enforceability, to general principles of equity.

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(d) Other than the filings, notices and reports pursuant to, in compliance with or required to be made under the Exchange Act, no filings, notices, reports, consents, registrations, approvals, permits, waivers, expirations of waiting periods or authorizations are required to be obtained by the Sponsor from, or to be given by the Sponsor to, or be made by the Sponsor with, any Governmental Authority in connection with the execution, delivery and performance by the Sponsor of this Agreement, the consummation of the transactions contemplated hereby or the Merger and the other transactions contemplated by the BCA.

(e) The execution, delivery and performance of this Agreement by the Sponsor does not, and the consummation of the transactions contemplated hereby or the Merger and the other transactions contemplated by the BCA will not, constitute or result in (i) a breach or violation of, or a default under, the limited liability company agreement or similar governing documents of the Sponsor, (ii) with or without notice, lapse of time or both, a breach or violation of, a termination (or right of termination) of or a default under, the loss of any benefit under, the creation, modification or acceleration of any obligations under or the creation of a Lien on any of the properties, rights or assets of the Sponsor pursuant to any contract binding upon the Sponsor or (iii) any change in the rights or obligations of any party under any contract legally binding upon the Sponsor, except, in the case of clause (ii) or (iii) directly above, for any such breach, violation, termination, default, creation, acceleration or change that would not, individually or in the aggregate, reasonably be expected to prevent or materially delay or impair the Sponsor’s ability to perform its obligations hereunder or to consummate the transactions contemplated hereby, the consummation of the Merger or the other transactions contemplated by the BCA.

(f) As of the date of this Agreement, there is no action, proceeding or investigation pending against the Sponsor or, to the knowledge of the Sponsor, threatened against the Sponsor that questions the beneficial or record ownership of the Sponsor Shares, the validity of this Agreement or the performance by the Sponsor of its obligations under this Agreement.

(g) The Sponsor understands and acknowledges that each of BCAC and the Company is entering into the BCA in reliance upon the Sponsor’s execution and delivery of this Agreement and the representations, warranties, covenants and other agreements of the Sponsor contained herein

6. Further Assurances. From time to time, at either BCAC’s or the Company’s request and without further consideration, the Sponsor shall execute and deliver such additional documents and take all such further action as may be reasonably necessary or reasonably requested to effect the actions and consummate the transactions contemplated by this Agreement.

7. Amendment and Modification. This Agreement may not be amended, modified or supplemented in any manner, whether by course of conduct or otherwise, except by an instrument in writing signed by the Sponsor, BCAC and the Company.

8. Waiver. No failure or delay by any party hereto exercising any right, power or privilege hereunder shall operate as a waiver thereof nor shall any single or partial exercise thereof preclude any other or further exercise thereof or the exercise of any other right, power or privilege. The rights and remedies of the parties hereto hereunder are cumulative and are not exclusive of any rights or remedies which they would otherwise have hereunder. Any agreement on the part of a party hereto to any such waiver shall be valid only if set forth in a written instrument executed and delivered by such party.

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9. Notices. All notices and other communications hereunder shall be in writing and shall be deemed given if delivered personally, by email (with confirmation of receipt) or sent by a nationally recognized overnight courier service to the parties hereto at the following addresses (or at such other address for a party as shall be specified by like notice made pursuant to this Section 9):

if to Sponsor, BCAC or Merger Sub:

Brookline Capital Acquisition Corp.

280 Park Avenue, Suite 43W

New York, NY 10017

Attention: Samuel P. Wertheimer, Chairman and CEO

Email: ***

with a copy to:

DLA Piper LLP (US)

1251 Avenue of the Americas

New York, NY 10020

Attention: James Kelly; Peter Ekberg

Email: ***@***; ***@***

and

DLA Piper LLP (US)

555 Mission Street

Suite 2400

San Francisco, CA 94105

Attention: Jeffrey Selman

Email: ***@***

if to the Company:

Apexigen, Inc.

75 Shoreway Road

Suite C

San Carlos, CA 94070

Attention: Xiaodong Yang, MD, PhD, President and CEO;

                Amy Wong, Senior Vice President, Finance and Operations

Email: ***

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with a copy to:

Wilson Sonsini

650 Mill Page Road

Palo Alto, CA 94304

Attention: Kenneth A. Clark; Michael E. Coke; Lance E. Brady

Email: ***@***; ***@***; ***@***

and with a copy to:

Wilson Sonsini

One Market Plaza, Spear Tower, Suite 3300

San Francisco, CA 94105

Attention: Robert T. Ishii

Email: ***@***

10. Entire Agreement. This Agreement, the BCA and the Transaction Documents constitute the entire agreement and supersede all prior agreements and understandings, both written and oral, among the parties hereto with respect to the subject matter hereof and thereof.

11. No Third-Party Beneficiaries. The Sponsor hereby agrees that its representations, warranties and covenants set forth herein are solely for the benefit of BCAC and the Company in accordance with and subject to the terms of this Agreement, and this Agreement is not intended to, and does not, confer upon any person other than the parties hereto any rights or remedies hereunder, including, without limitation, the right to rely upon the representations and warranties set forth herein, and the parties hereto hereby further agree that this Agreement may only be enforced against, and any action that may be based upon, arise out of or relate to this Agreement, or the negotiation, execution or performance of this Agreement may only be made against, the persons expressly named as parties hereto.

12. Governing Law and Venue. This Agreement shall be governed by, interpreted under, and construed in accordance with the internal laws of the State of Delaware applicable to agreements made and to be performed within the State of Delaware, without giving effect to any choice-of-law provisions thereof that would compel the application of the substantive laws of any other jurisdiction

13. Assignment; Successors. Neither this Agreement nor any of the rights, interests or obligations hereunder shall be assigned by any of the parties hereto in whole or in part (whether by operation of Law or otherwise) without the prior written consent of the other party, and any such assignment without such consent shall be null and void. This Agreement shall be binding upon, inure to the benefit of and be enforceable by the parties hereto and their respective successors and permitted assigns.

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14. No Recourse. Notwithstanding anything to the contrary contained herein or otherwise, but without limiting any provision in the BCA or any other Transaction Document, this Agreement may only be enforced against, and any claims or causes of action that may be based upon, arise out of or relate to this Agreement, or the negotiation, execution or performance of this Agreement or the transactions contemplated hereby, may only be made against the entities and Persons that are expressly identified as parties to this Agreement in their capacities as such and no former, current or future shareholders or stockholders, equity holders, controlling persons, directors, officers, employees, general or limited partners, members, managers, agents or affiliates of any party hereto, or any former, current or future direct or indirect shareholder or stockholder, equity holder, controlling person, director, officer, employee, general or limited partner, member, manager, agent or affiliate of any of the foregoing (each, a “Non-Recourse Party”) shall have any liability for any obligations or liabilities of the parties to this Agreement or for any claim (whether in tort, contract or otherwise) based on, in respect of, or by reason of, the transactions contemplated hereby or in respect of any oral representations made or alleged to be made in connection herewith. Without limiting the rights of any party against the other parties hereto, in no event shall any party or any of its affiliates seek to enforce this Agreement against, make any claims for breach of this Agreement against, or seek to recover monetary damages from, any Non-Recourse Party.

15. Specific Performance. Each party acknowledges and agrees that the other parties hereto would be irreparably harmed and would not have any adequate remedy at law in the event that any of the provisions of this Agreement were not performed in accordance with their specific terms or were otherwise breached. Accordingly, each party agrees that the other parties hereto shall be entitled to an injunction or injunctions to prevent breaches of this Agreement and to enforce specifically the terms and provisions of this Agreement, this being in addition to any other remedy to which such parties are entitled at law or in equity.

16. Severability. In the event that any provision of this Agreement or the application thereof becomes or is declared by a court of competent jurisdiction to be illegal, void or unenforceable, the remainder of this Agreement will continue in full force and effect and the application of such provision to other persons or circumstances will be interpreted so as reasonably to effect the intent of the parties hereto.

17. Counterparts. This Agreement may be executed in one or more counterparts, all of which shall be considered one and the same agreement, it being understood that each party need not sign the same counterpart. This Agreement shall become effective when each party shall have received a counterpart hereof signed by all of the other parties. Signatures delivered electronically or by facsimile shall be deemed to be original signatures.

18. Survival of Representations and Warranties. None of the representations and warranties made by the parties hereto in this Agreement shall survive the Closing.

19. Headings and Captions. The headings and captions of the various subdivisions of this Agreement are for convenience of reference only and shall in no way modify or affect the meaning or construction of any of the terms or provisions hereof.

20. Construction. The words “include,” “includes,” and “including” will be deemed to be followed by “without limitation.” Pronouns in masculine, feminine, and neuter genders will be construed to include any other gender, and words in the singular form will be construed to include the plural and vice versa, unless the context otherwise requires. The words “this Agreement,”

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“herein,” “hereof,” “hereby,” “hereunder,” and words of similar import refer to this Agreement as a whole and not to any particular subdivision unless expressly so limited. The word “or” shall be disjunctive but not exclusive. The parties hereto intend that each representation, warranty, and covenant contained herein will have independent significance. If any party hereto has breached any representation, warranty, or covenant contained herein in any respect, the fact that there exists another representation, warranty or covenant relating to the same subject matter (regardless of the relative levels of specificity) which such party has not breached will not detract from or mitigate the fact that such party is in breach of the first representation, warranty, or covenant.

21. Mutual Drafting. This Agreement is the joint product of the parties hereto and each provision hereof has been subject to the mutual consultation, negotiation and agreement of the parties hereto and shall not be construed for or against any party.

22. No Ownership Interest. Nothing contained in this Agreement shall be deemed to vest in the Company, or any of its affiliates or Representatives, any direct or indirect ownership or incidence of ownership of or with respect to any Sponsor Shares.

23. No Partnership, Agency or Joint Venture. This Agreement is intended to create a contractual relationship among Sponsor and the Company, and is not intended to create, and does not create, any agency, partnership, joint venture or any like relationship between or among the parties.

24. Termination. This Agreement shall terminate upon the earliest of (i) the termination of the BCA in accordance with its terms, and (ii) the time this Agreement is terminated upon the mutual written agreement of BCAC, the Company and the Sponsor (the earliest such date under clause (i) and (ii) being referred to herein as the “Termination Date”); provided, that the provisions set forth in Sections 1, 3 and 4 shall no longer be effective from and after the Closing of the Merger; provided further, that the provisions set forth in Sections 9 through 24 shall survive the Termination Date.

[Signature Pages Follow]

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IN WITNESS WHEREOF, the parties hereto have caused this Agreement to be executed (where applicable, by their respective officers or other authorized persons thereunto duly authorized) as of the date first written above.

[Signature Page to Sponsor Support Agreement]