Compass Therapeutics, Inc.

80 GUEST STREET, SUITE 601

BOSTON, MA 02135

PROXY STATEMENT

FOR THE 2024 ANNUAL MEETING OF STOCKHOLDERS

TO BE HELD JUNE 13, 2024

This proxy statement contains information about the 2024 Annual Meeting of Stockholders (the “Annual Meeting”) of Compass Therapeutics, Inc., which will be held on June 13, 2024 at 10:00 a.m. Eastern Time. The Annual Meeting will be a virtual meeting. You will be able to attend and participate in the Annual Meeting online by registering at www.virtualshareholdermeeting.com/CMPX2024.

The Board of Directors of Compass Therapeutics, Inc. is using this proxy statement to solicit proxies for use at the Annual Meeting. In this proxy statement, the terms “Compass,” “we,” “us,” and “our” refer to Compass Therapeutics, Inc. The mailing address of our principal executive offices is Compass Therapeutics, Inc., 80 Guest Street, Suite 601, Boston, MA 02135.

Only Compass Therapeutics, Inc. stockholders of record at the close of business on April 17, 2024, will be entitled to vote at the Annual Meeting and any adjournment or postponement thereof. All stockholders as of the record date, or their duly appointed proxies, may attend the meeting.

To be admitted to the Annual Meeting and vote your shares, you must register at www.virtualshareholdermeeting.com/CMPX2024. You will be required to enter the control number provided on the proxy card and beneficial owners of shares held in street name will need to follow the instructions provided in the voting instructions form by the broker, bank or other nominee that holds their shares. Upon completing your registration, you will receive further instructions via email, including unique links to access the Annual Meeting and to submit questions in advance of the Annual Meeting. Please see the “General Information” section of the proxy statement for more details regarding the logistics of the virtual Annual Meeting, including the ability of stockholders to submit questions during the Annual Meeting, and technical details and support related to accessing the virtual platform.

If you are a stockholder of record, you can vote by proxy over the Internet (www.proxyvote.com) or by telephone (1-800-690-6903) by following the instructions provided in the proxy materials, or you can vote by mailing your proxy as described in the proxy materials. If your shares are held in street name, you will receive instructions from your broker or other nominee that holds your shares explaining how to vote your shares, and you may also have the choice of instructing the record holder as to the voting of your shares over the Internet or by telephone. Proxies submitted by mail must be received before the start of the Annual Meeting.

All properly submitted proxies will be voted in accordance with the instructions contained in those proxies. If no instructions are specified, the proxies will be voted in accordance with the recommendation of our Board of Directors with respect to each of the matters set forth in the accompanying Notice of Meeting. You may revoke your proxy at any time before it is exercised at the meeting by giving our corporate secretary written notice to that effect.

We are an “emerging growth company” under applicable federal securities laws and therefore are permitted to conform with certain reduced public company reporting requirements. As an emerging growth company, we provide in this proxy statement the scaled disclosure permitted under the Jumpstart Our Business Startups Act of 2012, including the compensation disclosures required of a “smaller reporting company,” as that term is defined in Rule 12b-2 promulgated under the Securities Exchange Act of 1934, as amended (the “Exchange Act”). In addition, as an emerging growth company, we are not required to conduct votes seeking approval, on an advisory basis, of the compensation of our named executive officers or the frequency with which such votes must be conducted. We will remain an “emerging growth company” until the earliest of (i) the last day of the fiscal year following the fifth anniversary of the date of the first sale of our common stock pursuant to an effective registration statement; (ii) the last day of the fiscal year in which our total annual gross revenue is equal to or more than $1.235 billion; (iii) the date on which we have issued more than $1 billion in nonconvertible debt during the previous three years; or (iv) the date on which we are deemed to be a large accelerated filer under the rules of the Securities and Exchange Commission (the “SEC”).

Even after we are no longer an “emerging growth company,” we may remain a “smaller reporting company.”

This proxy statement and our 2023 Annual Report to Stockholders are also available for viewing,

printing and downloading at:

https://investors.compasstherapeutics.com/financials-filing/annual-meeting

A copy of our Annual Report on Form 10-K for the fiscal year ended December 31, 2023, as filed with the SEC, except for exhibits, will be furnished without charge to any stockholder upon written request to Compass Therapeutics, Inc., 80 Guest Street, Suite 601, Boston, MA 02135, Attention: Corporate Secretary. This proxy statement and our Annual Report on Form 10-K for the fiscal year ended December 31, 2023 are also available on the SEC’s website atwww.sec.govor in the “Annual Meeting” item of the “Investors” section of our website at www.compasstherapeutics.com.