Dune Acquisition Corporation III

[_________], 2026

Dune Acquisition Holdings III LLC
700 S. Rosemary Avenue, Suite 204
West Palm Beach, FL 33401

	Re:	Administrative Services Agreement

Ladies and Gentlemen:

This letter agreement by and between Dune Acquisition Corporation III (the “Company”) and Dune Acquisition Holdings III LLC (the “Sponsor”), dated as of the date hereof, will confirm our agreement that, commencing on the date the securities of the Company are first listed on the Nasdaq Global Market (the “Listing Date”), pursuant to a Registration Statement on Form S-1 and prospectus filed with the U.S. Securities and Exchange Commission (the “Registration Statement”) and continuing until the earlier of the consummation by the Company of an initial business combination and the Company’s liquidation (in each case as described in the Registration Statement) (such earlier date hereinafter referred to as the “Termination Date”):

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INVESTMENT MANAGEMENT TRUST AGREEMENT

This Investment Management Trust Agreement (this “Agreement”) is made effective as of [_________], 2026 by and between Dune Acquisition Corporation III, a Cayman Islands exempted company (the “Company”), and Continental Stock Transfer & Trust Company, a New York corporation (the “Trustee”).

WHEREAS, the Company’s registration statement on Form S-1 (File No. 333-293667) (the “Registration Statement”) and prospectus (the “Prospectus”) for the initial public offering of the Company’s units (the “Units”), each of which consists of one of the Company’s Class A ordinary shares, par value $0.0001 per share (the “Ordinary Shares”), and one-half of one redeemable warrant, each whole warrant entitling the holder thereof to purchase one Ordinary Share (such initial public offering hereinafter referred to as the “Offering”), has been declared effective as of the date hereof by the U.S. Securities and Exchange Commission;

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REGISTRATION RIGHTS AGREEMENT

THIS REGISTRATION RIGHTS AGREEMENT (this “Agreement”), dated as of [_________], 2026, is made and entered into by and among Dune Acquisition Corporation III, a Cayman Islands exempted company (the “Company”), Dune Acquisition Holdings III LLC, a Delaware limited liability company (the “Sponsor”), and each of the undersigned parties listed on the signature page hereto under “Holders” (each such party, together with the Sponsor and any person or entity who hereafter becomes a party to this Agreement pursuant to Section 5.2 of this Agreement, a “Holder” and collectively the “Holders”).

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RECITALS

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WHEREAS, the Company has 5,750,000 Class B ordinary shares, par value $0.0001 per share (the “Founder Shares”), issued and outstanding, up to 750,000 of which will be surrendered to the Company for no consideration depending on the extent to which the underwriters of the Company’s initial public offering exercise their over-allotment option;

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PRIVATE PLACEMENT WARRANTS PURCHASE AGREEMENT

THIS PRIVATE PLACEMENT WARRANTS PURCHASE AGREEMENT, dated as of [_________], 2026 (as it may from time to time be amended, this “Agreement”), is entered into by and between Dune Acquisition Corporation III, a Cayman Islands exempted company (the “Company”), and Dune Acquisition Holdings III LLC, a Delaware limited liability company (the “Purchaser”).

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WHEREAS, the Company intends to consummate an initial public offering of the Company’s units (the “Public Offering”), each unit consisting of one Class A Ordinary Share, par value $0.0001 per share, of the Company (an “Ordinary Share”), and one-half of one redeemable warrant. Each whole warrant entitles the holder to purchase one Ordinary Share at an exercise price of $11.50 per Ordinary Share. The Purchaser has agreed to purchase an aggregate of 1,300,000 warrants (whether or not the underwriter’s over-allotment option is exercised) (the “Private Placement Warrants”), each Private Placement Warrant entitling the holder to purchase one Ordina

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THIS PROMISSORY NOTE (“NOTE”) HAS NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED (THE “SECURITIES ACT”). THIS NOTE HAS BEEN ACQUIRED FOR INVESTMENT ONLY AND MAY NOT BE SOLD, TRANSFERRED OR ASSIGNED IN THE ABSENCE OF REGISTRATION OF THE RESALE THEREOF UNDER THE SECURITIES ACT OR AN OPINION OF COUNSEL REASONABLY SATISFACTORY IN FORM, SCOPE AND SUBSTANCE TO THE COMPANY THAT SUCH REGISTRATION IS NOT REQUIRED.

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AMENDED AND RESTATED PROMISSORY NOTE

Principal Amount: Up to $200,000	Dated as of July 22, 2026

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SECURITIES TRANSFER AGREEMENT

This Securities Transfer Agreement (this “Agreement”) is entered into as of July [__], 2026 by and between DUNE ACQUISITION HOLDINGS III LLC (the “Transferor”) and Clear Street LLC (the “Transferee””).

RECITALS

WHEREAS, the Transferor desires to sell 200,000 Class B Ordinary shares, $0.0001 par value per share (the “Shares”) of Dune Acquisition Corporation III (the “Company”) to the Transferee in connection with the Company’s initial public offering (“IPO”) of units of the Company.

NOW, THEREFORE, the parties hereto, for good and valuable consideration which each party acknowledges the receipt of, hereby agree as follows:

1. Transfer of the Securities.

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**PRIVATE PLACEMENT UNITS SUBSCRIPTION AGREEMENT **

This Private Placement Units Subscription Agreement (this “Agreement”) is made as of this [•] day of [•], 2026, by and between BOA Acquisition Corp. II, a Cayman Islands exempted company (the “Company”), Bet on America II Sponsor LLC, a Cayman Islands limited liability company (the “Sponsor”), for itself and on behalf of the several purchasers named on Exhibit A hereto (collectively, the “Purchasers”).

WHEREAS, the Company desires to sell to the Sponsor, on a private placement basis (the “Offering”), an aggregate of 201,500 units (the “Private Placement Units”) of the Company, each Private Placement Unit comprised of one Class A ordinary share of the Company, par value $0.0001 per share (the “Class****** A Ordinary Shares**”), and one right (the “Rights”) to receive one Class A Ordinary Share (the “Rights Shares”) upon consummation of the Company’s initial Business Combination (as defined below), for an aggregate purchase price of $2,015,000;

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Exhibit: 10.32

RESTRICTED STOCK AWARD AGREEMENT

UNDER THE Apnimed, Inc.

2026 STOCK OPTION AND INCENTIVE PLAN

Name of Grantee:
No. of Shares:
Grant Date:

Pursuant to the Apnimed, Inc. 2026 Stock Option and Incentive Plan (the “Plan”) as amended through the date hereof, Apnimed, Inc. (the “Company”) hereby grants a Restricted Stock Award (an “Award”) to the Grantee named above. Upon acceptance of this Award, the Grantee shall receive the number of shares of Common Stock, par value $0.00001 per share (the “Stock”) of the Company specified above, subject to the restrictions and conditions set forth herein and in the Plan. The Company acknowledges the receipt from the Grantee of consideration with respect to the par value of the Stock in the form of cash, past or future services rendered to the Company by the Grantee or such other form

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APNIMED, INC.

2026 EMPLOYEE STOCK PURCHASE PLAN

The purpose of the Apnimed, Inc. 2026 Employee Stock Purchase Plan (the “Plan”) is to provide eligible employees of Apnimed, Inc. (the “Company”) and each Designated Company (as defined in Section 11) with opportunities to purchase shares of the Company’s common stock, par value $0.00001 per share (the “Common Stock”). 558,767 shares of Common Stock in the aggregate have been approved and reserved for this purpose, plus on January 1, 2027 and each January 1 thereafter until the Plan terminates pursuant to Section 20, the number of shares of Common Stock reserved and available for issuance under the Plan shall be cumulatively increased by the least of (i) 1,676,301 shares of Common Stock, (ii) 1% of the number of Outstanding Shares on the immediately preceding December 31, and (iii) such lesser number of shares of Common Stock as determined by the Administrator (as defined in Section 1). The Plan includes two components: a Code Section 423 Component (the “423 Component”) and a non-Code Section 423 Component (the “Non-423 Component”). I

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STOCK OPTION AGREEMENT

FOR COMPANY EMPLOYEES AND CONSULTANTS

UNDER THE APNIMED, INC.

2026 STOCK OPTION AND INCENTIVE PLAN

Name of Optionee:
No. of Option Shares:
Option Exercise Price per Share:	$
Type of Option:	[Incentive Stock Option][Non-Qualified Stock Option]
Grant Date:
Expiration Date:

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APNIMED, INC.

2026 STOCK OPTION AND INCENTIVE PLAN

SECTION 1. GENERAL PURPOSE OF THE PLAN; DEFINITIONS

The name of the plan is the Apnimed, Inc. 2026 Stock Option and Incentive Plan (as amended from time to time, the “Plan”). The purpose of the Plan is to encourage and enable the officers, employees, Non-Employee Directors and Consultants of Apnimed, Inc. (the “Company”) and its Affiliates upon whose judgment, initiative and efforts the Company largely depends for the successful conduct of its business to acquire a proprietary interest in the Company. It is anticipated that providing such persons with a direct stake in the Company’s welfare will assure a closer identification of their interests with those of the Company and its stockholders, thereby stimulating their efforts on the Company’s behalf and strengthening their desire to remain with the Company or one of its Affiliates.

The following terms shall be defined as set forth below:

“Act”means the U.S. Securities Act of 1933, as amended, and the rules and regulations thereunder.

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TWENTY-FIFTH AMENDMENT TO THE

2017 STOCK INCENTIVE PLAN

OF

APNIMED, INC.

July 22, 2026

This Twenty-Fifth Amendment to the 2017 Stock Incentive Plan (the “Plan”) of Apnimed, Inc., a Delaware corporation (the “Company”) is made pursuant to Section 11(d) of the Plan as of the date first written above.

Recitals:

WHEREAS, the Board of Directors of the Company has determined that it is in the best interest of the Company and its stockholders to increase the number of authorized shares available under the Plan.

NOW THEREFORE, Section 4(a) titled “Stock Available for Awards” is hereby amended as follows:

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