Exhibit 23.1

Consent of Independent Registered Public Accounting Firm

We consent to the incorporation by reference in this Registration Statement on Form S-3 and related Prospectuses, of our report dated March 21, 2024, with respect to the consolidated financial statements of Compass Therapeutics, Inc. and Subsidiaries as of December 31, 2023 and 2022, and for the years then ended, which report is included in the Annual Report on Form 10-K of Compass Therapeutics, Inc. for the year ended December 31, 2023, filed with the Securities and Exchange Commission. We also consent to the reference to our firm under the caption “Experts.”

/s/ CohnReznick LLP

Melville, New York

August 30, 2024