United States securities and exchange commission logo August 14, 2020 Vered Bisker-Leib Chief Operating Officer Compass Therapeutics, Inc. 245 First Street 3rd Floor Cambridge, Massachusetts 02142 Re: Compass Therapeutics, Inc. Registration Statement on Form S-1 Filed August 11, 2020 File No. 333-244353 Dear Dr. Bisker-Leib: 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 Margaret Schwartz at 202-551-7153 with any questions. Sincerely, Division of Corporation Finance Office of Life Sciences