completist
n. A person who obsessively gathers the complete collection of a particular set of items (such as a musician's recordings or an author's books).

Example Citation:
"Hendrix completists, and they are legion, already will have these volumes cataloged with previous versions on quadraphonic vinyl, 8-track and Betamax."
—Bill Lammers, "Latest CD Offers More of Hendrix," The Plain Dealer, July 25, 1999

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