United States securities and exchange commission logo July 15, 2021 Thomas J. Schuetz, M.D., Ph.D. Chief Executive Officer Compass Therapeutics, Inc. 80 Guest Street Suite 601 Boston, MA 02135 Re: Compass Therapeutics, Inc. Registration Statement on Form S-3 Filed July 9, 2021 File No. 333-257821 Dear Dr. Schuetz: This is to advise you that we have not reviewed and will not review your registration statement. Please refer to Rules 460 and 461 regarding requests for acceleration. We remind you that the company and its management are responsible for the accuracy and adequacy of their disclosures, notwithstanding any review, comments, action or absence of action by the staff. Please contact Gary Guttenberg at 202-551-6477 with any questions. Sincerely, Division of Corporation Finance Office of Life Sciences cc: Richard A. Hoffman, Esq.