Exhibit 10.35

[***] Certain identified information has been excluded from this exhibit because (i) it is not material and (ii) is the type that Pulmatrix treats as private or confidential.

Palladium Capital Group, LLC

Carnegie Hall Tower

152 West 57^TH Street, Floor 24

New York, NY 10019

Tel (646) 485-7297

JP@Palladiumcapital.Com

March 23, 2026

Kevin Slawin, M.D., Chief Executive Officer

Eos SENOLYTIX, Inc.

[***]

Dear Dr. Slawin:

This letter agreement (this “Agreement”) sets forth the understanding and agreement between PALLADIUM CAPITAL GROUP, LLC, a Delaware limited liability company (“Palladium”), and EOS SENOLYTIX, INC., a Delaware corporation (the “Company”), with respect to the following:

1. The Company hereby engages Palladium as its advisor in connection with the contemplated reverse merger (the “Merger”) between the Company and Pulmatrix, Inc., a Delaware corporation (“Pulmatrix”), pursuant to which Pulmatrix will acquire the Company. Palladium will provide such advisory services as may be reasonably requested by the Company in connection with the Merger.

Palladium acknowledges and agrees that the Company shall have the right, in its sole discretion, to both reject any Palladium Investor’s participation in a Transaction or to altogether abandon a Transaction. It is understood that Palladium’s assistance in a Transaction will be subject to the satisfactory completion of such reasonable investigation and inquiry into the relevant affairs of the Company as Palladium deems appropriate under the circumstances and to the receipt of all internal approvals of Palladium in connection with the Transaction. The execution of this Agreement does not constitute a commitment by Palladium to purchase any Securities and does not ensure a successful Transaction of the Securities or of the success of Palladium with respect to securing any other financing on behalf of the Company.

2. Palladium’s engagement as advisor in connection with the Merger shall commence as of the date hereof and shall terminate upon the closing of the Merger. Either party may terminate this Agreement prior to the closing of the Merger upon thirty (30) days’ prior written notice to the other party. Notwithstanding any such termination, if the Merger is subsequently consummated, the Advisory Fee shall remain payable in full in accordance with Section 3.

3. In consideration of Palladium’s advisory services in connection with the Merger, the Company shall pay Palladium an advisory fee of Five Hundred Thousand Dollars ($500,000) (the “Advisory Fee”), payable as follows: (a) Two Hundred Fifty Thousand Dollars ($250,000) shall be payable in cash by wire transfer upon the closing of the Merger; and (b) Two Hundred Fifty Thousand Dollars ($250,000) shall be payable in cash by wire transfer upon the earlier to occur of (i) the one-year anniversary of the closing of the Merger, or (ii) the date on which the Combined Company raises at least Ten Million Dollars ($10,000,000) of additional equity capital (including convertible debt) following the closing of the Merger. If any portion of the Advisory Fee is not paid when due, such unpaid amount shall accrue interest at the rate of 1.5% per month, calculated retroactively from the date such payment was due, until paid in full. Palladium shall not be entitled to reimbursement of any expenses incurred in connection with the performance of its services under this Agreement.

The Company acknowledges that Palladium has entered into an M&A Advisory Agreement dated February 12, 2026 with Pulmatrix (the “Pulmatrix Agreement”), pursuant to which Pulmatrix has agreed to issue to Palladium shares of Pulmatrix common stock equal to three percent (3%) of the total number of shares of common stock of Pulmatrix outstanding on a fully diluted basis immediately following the closing of the Merger (such shares, the “Merger Shares”).

4. The Company shall provide indemnification as set forth in Annex A attached hereto and made a part hereof.

5. The provisions of Sections 3, 4, and 5 (including, without limitation, the provisions of indemnification referred to in Section 4) shall survive the expiration or termination of this Agreement.

6. The Company may provide Palladium with written materials and information concerning the Company’s business, operations, assets, liabilities and receivables (the “Materials”). Palladium acknowledges that it shall (a) use the Materials solely for the purpose of performing its advisory services in connection with the Merger, (b) keep all Materials confidential in accordance with any confidentiality or non-disclosure agreement between the parties, and (c) not disclose any Materials to any third party without the prior written consent of the Company. Subject to the accuracy and completeness of the underlying Materials provided by the Company, Palladium shall be responsible for the accuracy and completeness of any advice or analysis it provides to the Company based on the Materials. The Company represents and warrants to Palladium that, to the knowledge of the Company, all Materials provided to Palladium will be, when provided, true, complete and accurate in all material respects and will not contain any untrue statement of a material fact or omit to state a material fact necessary in order to make the statements therein not misleading in light of the circumstances under which such statements are made. If at any time prior to the completion of the Merger an event occurs which would cause the Materials (as supplemented or amended) to contain an untrue statement of a material fact or to omit to state a material fact necessary in order to make the statements therein, in light of the circumstances under which they were made, not misleading, the Company will promptly notify Palladium of such event. “Materials” shall not include information that is independently produced by Palladium and not based on materials provided by the Company or information available from generally recognized public sources.

7. Palladium represents and warrants as follows: Palladium is registered as a broker/dealer with the SEC pursuant to Section 15(b) of the Securities Exchange Act of 1934, as amended (the “Exchange Act”), and is a member in good standing of the Financial Industry Regulatory Authority (“FINRA”), and such SEC registration and FINRA membership is currently in effect and has not been withdrawn, cancelled or revoked. Palladium is registered and/or licensed as a broker/dealer in each state in which it conducts activities that require such registration or licensure. Palladium agrees to perform its duties and obligations hereunder in a manner consistent with any instructions given by the Company, the terms of this Agreement and the provisions of all laws, rules and regulations that are applicable to Palladium and its business, including, without limitation, the Exchange Act, the Securities Act of 1933, as amended (the “Securities Act”), and the rules and regulations of FINRA and any other applicable self-regulatory organizations.

Based upon a diligent inquiry, each of Palladium and the Company represents and warrants to the other, and agrees, that neither it, nor any of its directors, executive officers, other officers or employees participating in the offering of Securities, general partners or managing members, or any of the directors, executive officers or other officers participating in the offering of Securities of any such general partner or managing member (each, a “Covered Person”), is subject to any of the “Bad Actor” disqualifications described in Rule 506(d)(1)(i) to (viii) under the Securities Act (a “Disqualification Event”), except for a Disqualification Event (i) contemplated by Rule 506(d)(2) of the Securities Act and (ii) a description of which has been furnished in writing to the other on or prior to execution hereof.¹ Each of Palladium and the Company shall provide prompt written notice to the other of any Disqualification Event relating to any Covered Person, or any event that would, with the passage of time, become a Disqualification Event, prior to each Closing. Each of Palladium and the Company represents and warrants to the other that it is not aware of any person other than a Covered Person that has been or will be paid (directly or indirectly) remuneration for solicitation of purchasers in connection with the sale of Securities.

8. The Company acknowledges that Palladium is also acting as advisor to Pulmatrix in connection with the Merger pursuant to the Pulmatrix Agreement. The Company acknowledges and consents to Palladium’s engagement by Pulmatrix and waives any conflict of interest arising therefrom. Palladium shall not be obligated to disclose to the Company any confidential information obtained from Pulmatrix, or to Pulmatrix any confidential information obtained from the Company, except to the extent required by applicable law or regulation. The Company further acknowledges that Palladium will receive separate compensation from Pulmatrix in connection with such engagement, consisting of the Merger Shares as described in Section 3 of this Agreement.

¹ USA Patriot Act Disclosure: Federal law requires all financial institutions to obtain, verify, and record information that identifies each person who opens an account or transacts business with a financial institution. Palladium may require Company information from individuals authorized to transact business on behalf of the Company. Requested items could include Driver’s license number, passport number, U.S. Taxpayer Identification (ID) Number, Alien ID Card, and any other government-issued document evidencing nationality or residence. Failure to produce the requested information in a timely manner may prohibit Palladium from conducting a transaction on behalf of Company.

9. Upon a Closing, the Company agrees that Palladium has the right to place notices and/or advertisements in financial and other newspapers and journals (whether in print or on the Internet), and to publicize on Palladium’s own website and/or marketing materials, at its own expense, describing its services to the Company hereunder. Furthermore, promptly after a Closing, the Company shall provide Palladium with a full and complete set of closing documents pertaining to such Closing, including but not limited to copies of any fully executed subscription documents, transaction agreements, ancillary documents, and closing statements. Such closing documents shall be held in confidence by Palladium under terms of confidentiality no less than those governing other confidential information subject to any NDA (or similar) agreement to which Palladium and Company are parties.

10. Nothing contained in this Agreement shall limit or restrict the right of Palladium or of any member, employee, agent or representative of Palladium, to be a shareholder, member, partner, director, officer, employee, agent or representative of, or to engage in, any other business, whether or not of a similar nature of the Company’s business, nor to limit or restrict the right of Palladium to render services of any kind to any other corporation, company, firm, individual or association. The Company acknowledges that Palladium and its affiliates may have and may continue to have investment banking and other relationships with parties other than the Company pursuant to which Palladium may acquire information of interest to the Company. Palladium shall have no obligation to disclose such information to the Company or to use such information in connection with any contemplated transaction.

11. The failure or neglect of either of the parties hereto to enforce any of its rights or to insist, in any one or more instances, upon the strict performance of any of the terms or conditions of this Agreement, or its waiver of strict performance of any of the terms or conditions of this Agreement, shall not be construed as a waiver or relinquishment in the future of such term or condition, but the same shall continue in full force and effect.

12. Any notices hereunder shall be given in writing and shall be sent to the Company and to Palladium at their respective mailing addresses set forth above by reputable overnight courier such as FedEx with a copy to Palladium by email at JP@PalladiumCapital.com. Either party may designate any other address to which notice shall be given by giving written notice to the other party of such change of address in the manner herein provided.

13. Each party hereby represents and warrants to the other party that it has the full and complete power and authority to enter into this Agreement, that all required action has been taken by it as is necessary to authorize it to enter into this Agreement, that, upon the execution of this Agreement by the other party hereto, it is fully bound by the terms hereof, and that the person executing this agreement on its behalf is authorized to do so and does bind the undersigned hereto without requiring the joinder or further approval of any other person whomsoever.

14. The Company acknowledges and agrees that Palladium has been retained to act solely as an independent contractor and in such capacity shall not act as an employee of the Company or as an agent of the Company other than specifically provided herein.

15. This Agreement shall inure to the benefit of and be binding upon the respective Affiliates, successors and assigns of the parties hereto. The term “Affiliates” shall mean, with respect to any person or entity, any other person or entity who, directly or indirectly, through one or more intermediaries controls, is controlled by, or is under common control with such person or entity and any spouse, parent or issue of any such person; “control” means the power, directly or indirectly, to direct or cause the direction of the management and policies of a person or entity whether through ownership of voting securities, by contract or otherwise.

16. THE PARTIES HERETO AGREE THAT ALL DISPUTES ARISING FROM OR RELATING TO THE AGREEMENT WILL BE RESOLVED BY ARBITRATION IN NEW YORK CITY PURSUANT TO THE ARBITRATION RULES OF FINRA WITH RESPECT TO DISPUTES BETWEEN FINRA MEMBERS AND THEIR CUSTOMERS. THIS AGREEMENT CONTAINS A PREDISPUTE ARBITRATION CLAUSE. BY SIGNING THIS AGREEMENT, THE PARTIES AGREE AS FOLLOWS:

(1) All parties to this Agreement are giving up the right to sue each other in court, including the right to a trial by jury, except as provided by the rules of the arbitration forum in which a claim is filed.

(2) Arbitration awards are generally final and binding; a party’s ability to have a court reverse or modify an arbitration award is very limited.

(3) The ability of the parties to obtain documents, witness statements and other discovery is generally more limited in arbitration than in court proceedings.

(4) The arbitrators do not have to explain the reason(s) for their award unless, in an eligible case, a joint request for an explained decision has been submitted by all parties to the panel at least 20 days prior to the first scheduled hearing date.

(5) The panel of arbitrators may include a minority of arbitrators who were or are affiliated with the securities industry.

(6) The rules of some arbitration forums may impose time limits for bringing a claim in arbitration. In some cases, a claim that is ineligible for arbitration may be brought in court.

(7) The rules of the arbitration forum in which the claim is filed, and any amendments thereto, shall be incorporated into this Agreement.

17. This Agreement shall be construed and governed in accordance with the laws of the State of New York.

18. This Agreement contains the entire agreement between the parties, may not be altered or modified, except in writing and signed by the party to be charged thereby, and supersedes any and all previous agreements between the parties relating to the subject matter hereof.

19. Palladium acknowledges that it is not granted any right or authority to assume or create any obligation or liability or to make any representation, covenant, agreement or warranty, express or implied on the Company’s behalf, or to bind the Company in any matter whatsoever. Palladium will not have any rights or obligations in connection with the sale and purchase of the Securities contemplated by this Agreement except as expressly provided in this Agreement. In no event will Palladium be obligated to purchase the Securities to be purchased by Palladium Investors for its own account or for the accounts of its customers.

20. This Agreement may be executed in two or more counterparts, all of which when taken together shall be considered one and the same agreement and shall become effective when counterparts have been signed by each party and delivered to each other party, it being understood that the parties need not sign the same counterpart. In the event that any signature is delivered by facsimile transmission or by e-mail delivery of a “.pdf” format data file, such signature shall create a valid and binding obligation of the party executing (or on whose behalf such signature is executed) with the same force and effect as if such facsimile or “.pdf” signature page were an original thereof.

21. Palladium is not an expert on, and cannot render opinions regarding, legal, accounting, regulatory, or tax matters. The Company should consult with its other professional advisors concerning these matters before undertaking any transaction. All services, advice and information and reports provided by Palladium to the Company in connection with this assignment shall be for the sole benefit of the Company and shall not be relied upon by any other person.

[Signature page follows]

Palladium is delighted to accept this engagement and looks forward to working with you on this assignment. Please confirm that the foregoing correctly sets forth our understanding by signing below, whereupon this Agreement shall constitute a binding agreement as of the date first above written.

As set forth in Section 17 above, this Agreement contains an agreement to arbitrate disputes.

Annex A

Indemnification Provisions

In connection with the engagement of Palladium by the Company pursuant to the Agreement, the parties hereby agree as follows:

Annex B

Approved Palladium Investors

[To be updated from time to time upon mutual agreement of the parties.]