United States securities and exchange commission logo October 5, 2020 Charles Wilson, Ph.D. President and Chief Executive Officer Unum Therapeutics Inc. 200 Cambridge Park Drive, Suite 3100 Cambridge, Massachusetts 02140 Re: Unum Therapeutics Inc. Amendment No. 3 to Proxy Statement on Schedule 14A Filed October 2, 2020 File No. 001-38443 Dear Dr. Wilson: We have reviewed your amended filing and have the following comments. In some of our comments, we may ask you to provide us with information so we may better understand your disclosure. Please respond to these comments within ten business days by providing the requested information or advise us as soon as possible when you will respond. If you do not believe our comments apply to your facts and circumstances, please tell us why in your response. After reviewing your response to these comments, we may have additional comments. Amendment No. 2 to Proxy Statement on Schedule 14A Overview of Kiq, page 25 1. We note your revised disclosure in response to prior comment 1 that PLX9486 was in Phase II clinical development and the disclosure that this product candidate is a highly potent inhibitor. Please remove all statements that present your conclusions regarding the efficacy of your product candidate as this is a determination within the authority of the U.S. Food and Drug Administration and comparable regulatory bodies. 2. We note that in response to prior comment 2 you have included a redacted version of the license agreement with Plexxicon Inc. as annex to your proxy statement. Since it does not appear that you have filed the license agreement as an exhibit to one of the forms under the Securities Act or the Exchange Act that are designated in Item 601 of Regulation S-K, it is unclear which rule or regulation you are relying on to redact provisions from this agreement. Please advise. Please also disclose the aggregate amounts paid or received to date under agreement and the aggregate future potential milestone payments to be paid Charles Wilson, Ph.D. Unum Therapeutics Inc. October 5, 2020 Page 2 under the license agreement. 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 Tim Buchmiller at (202) 551-3635 or Celeste Murphy at (202) 551-3257 with any questions. Sincerely, FirstName LastNameCharles Wilson, Ph.D. Division of Corporation Finance Comapany NameUnum Therapeutics Inc. Office of Life Sciences October 5, 2020 Page 2 cc: Andrew H. Goodman, Esq. FirstName LastName