Exhibit 5.1

		Goodwin Procter LLP 100 Northern Avenue Boston, MA 02210
		goodwinlaw.com        +1 617 570 1000

March 20, 2020

Unum Therapeutics Inc.

200 Cambridge Park Drive, Suite 3100

Cambridge, MA 02140

Ladies and Gentlemen:

We have acted as counsel to Unum Therapeutics Inc., a Delaware corporation (the “Company”) in connection with the preparation of the prospectus supplement dated March 20, 2020, filed with the Securities and Exchange Commission (the “Commission”) pursuant to Rule 424(b) of the Securities Act of 1933, as amended (the “Securities Act”), which supplements Registration Statement on Form S-3 (File No. 333-230678) (as amended or supplemented, the “Registration Statement”) and the prospectus therein, in connection with the registration for offer and sale by the Company of up to $25,000,000 of shares of the Company’s common stock, par value $0.001 per share (the “Purchase Shares”), and the issuance of 726,382 shares of Common Stock (the “Commitment Shares” and together with the Purchase Shares, the “Shares”) to Lincoln Park Capital Fund, LLC as consideration for its commitment under the Purchase Agreement dated March 19, 2020 by and between the Company and Lincoln Park Capital Fund, LLC (the “Purchase Agreement”).

We have reviewed such documents and made such examination of law as we have deemed appropriate to give the opinion set forth below. We have relied, without independent verification, on certificates of public officials and, as to matters of fact material to the opinion set forth below, on certificates of officers of the Company.

For purposes of the opinion set forth below, we have assumed that no event occurs that causes the number of authorized shares of Common Stock available for issuance by the Company to be less than the number of then unissued Shares.

The opinion set forth below is limited to the Delaware General Corporation Law.

Based on the foregoing, we are of the opinion that the Shares have been duly authorized and, when issued in accordance with the Purchase Agreement, will be validly issued, fully paid and nonassessable.

Unum Therapeutics Inc.

March 20, 2020

Page 2

This opinion is being furnished to you for submission to the Commission as an exhibit to the Company’s Current Report on Form 8-K relating to the Shares (the “Current Report”), which is incorporated by reference in the Registration Statement. We hereby consent to the filing of this opinion letter as an exhibit to the Current Report and its incorporation by reference and the reference to our firm in that report. In giving our consent, we do not admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations thereunder.