LIMITED POWER OF ATTORNEY

    The undersigned hereby constitutes and appoints each of Chen Schor, Chief
Executive Officer of Adicet Bio, Inc., a Delaware corporation (the Company"),
Carrie Krehlik, Chief Human Resources Officer of the Company, Nick Harvey,
Chief Financial Officer of the Company, and Danielle Lauzon and Gabriela
Morales-Rivera both of Goodwin Procter LLP, signing singly, and with full
power of substitution, the undersigned's true and lawful attorney-in-fact to:

    (1)    execute for and on behalf of the undersigned, in the undersigned's
capacity as officer and/or director of the Company, from time to time the
following U.S. Securities and Exchange Commission ("SEC") forms: (i) Form ID,
including any attached documents (such as Update Passphrase Authentication),
to effect the assignment of codes to the undersigned to be used in the
transmission of information to the SEC using the EDGAR System; (ii) Form 3,
Initial Statement of Beneficial Ownership of Securities, including any
attached documents; (iii)Form 4, Statement of Changes in Beneficial Ownership
of Securities, including any attached documents; (iv) Form 5, Annual
Statement of Beneficial Ownership of Securities in accordance with Section
16(a) of the Securities Exchange Act of 1934, as amended, and the rules
thereunder, including any attached documents; (v) Schedules 13D and 13G; and
(vi) amendments of each thereof, in accordance with the Securities Exchange
Act of 1934, as amended, and the rules thereunder, including any attached
documents;

    (2)    do and perform any and all acts for and on behalf of the
undersigned which may be necessary or desirable to complete and execute any
such Form 3, 4 or 5, Schedule 13D or 13G, or any amendment(s) thereto and
timely file such form(s) with the SEC and any securities exchange, national
association or similar authority; and

    (3)    take any other action of any type whatsoever in connection with
the foregoing which, in the opinion of such attorney-in-fact, may be of
benefit to, in the best interest of, or legally required by, the undersigned,
it being understood that the documents executed by such attorney-in-fact on
behalf of the undersigned pursuant to this Power of Attorney shall be in such
form and shall contain such terms and conditions as such attorney-in-fact may
approve in such attorney-in-fact's discretion.

    The undersigned hereby grants to each such attorney-in-fact, acting
singly, full power and authority to do and perform any and every act and
thing whatsoever requisite, necessary or proper to be done in the exercise of
any of the rights and powers herein granted, as fully to all intents and
purposes as the undersigned might or could do if personally present, with
full power of substitution or revocation, hereby ratifying and confirming all
that such attorney-in-fact, or such attorney-in-fact's substitute or
substitutes, shall lawfully do or cause to be done by virtue of this power of
attorney and the rights and powers herein granted.  The undersigned
acknowledges that the foregoing attorneys-in-fact, in serving in such
capacity at the request of the undersigned, are not assuming, nor is the
Company assuming, any of the undersigned's responsibilities to comply with
Section 16 or Regulation 13D-G of the Securities Exchange Act of 1934, as
amended.  The undersigned hereby agrees to indemnify the attorneys-in-fact
and the Company from and against any demand, damage, loss, cost or expense
arising from any false or misleading information provided by the undersigned
to the attorneys-in-fact.
    This Power of Attorney shall remain in full force and effect until the
undersigned is no longer required to file such forms with respect to the
undersigned's holdings of and transactions in securities issued by the
Company, unless earlier revoked by the undersigned in a signed writing
delivered to the foregoing attorneys-in-fact.  This Power of Attorney
supersedes any prior power of attorney in connection with the undersigned's
capacity as an officer and/or director of the Company.  This Power of
Attorney shall expire as to any individual attorney-in-fact if such attorney-
in-fact ceases to be an employee of the Company.

    IN WITNESS WHEREOF, the undersigned has caused this Power of Attorney to
be executed as of October 27, 2020.

                                   /s/ Don Healey
                                   -----------------
                                   Name: Don Healey