POWER OF ATTORNEY

     The undersigned hereby constitutes and appoints Jean Liu, Todd Simpson,
Jessica Nielsen Causey and Jennifer Prosba, each of them, his or her true and
lawful attorney-in-fact to:

(1)  execute for and on behalf of the undersigned, in the undersigned's capacity
     as an officer, director, and/or person who holds more than 10% of the stock
     of Seagen Inc. (the "Company"), Forms 3, Forms 4 and Forms 5 in accordance
     with Section 16(a) of the Securities Exchange Act of 1934, as amended
     (the "Exchange Act"), and the rules thereunder;

(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 Forms 3,
     Forms 4 or Forms 5 and timely file any such forms with the United States
     Securities and Exchange Commission and any other 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-infact may approve in his or her discretion.

     The undersigned hereby grants to each such attorney-in-fact 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 his or her
substitute or substitutes, shall lawfully do or cause to be done pursuant to
this power of attorney. 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 of the Exchange Act.

     This Power of Attorney shall remain in full force and effect until the
undersigned is no longer required to file Forms 3, Forms 4, and Forms 5 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 attorneys-in-fact.

    The undersigned has caused this Power of Attorney to be executed as of this
9th day of November 2022.

                                           /s/ Sandra M. Swain M.D.
                                           -----------------------
                                           Sandra M. Swain, M.D.