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The Collaborative International Dictionary
outpope the Pope

outpope the Pope \out*pope" the Pope`\, v. i. To try to act as a more authentic member of a group than one who is a genuine member of the group; -- not necessarily in reference to religious matters; compare to be more Catholic than the Pope. [Colloq.]

Wiktionary
outpope the pope

vb. (context idiomatic English) To try to act as a more authentic member of a group than one who is a genuine member of the group.