Compass Therapeutics, Inc.

80 GUEST STREET, SUITE 601

BOSTON, MA 02135

PROXY STATEMENT

FOR THE 2026 ANNUAL MEETING OF STOCKHOLDERS

TO BE HELD JUNE 10, 2026

This proxy statement contains information about the 2026 Annual Meeting of Stockholders (the “Annual Meeting”) of Compass Therapeutics, Inc., which will be held on June 10, 2026 at 9:00 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/CMPX2026.

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 15, 2026, 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/CMPX2026. 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.

This proxy statement and our 2025 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, 2025, 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, 2025 are also available on the SEC’s website atwww.sec.govor in the “Financials – SEC Filings” section of the “Investors” section of our website at www.compasstherapeutics.com.

PROXY STATEMENT

FOR THE 2026 ANNUAL MEETING OF STOCKHOLDERS