1. To be or act more stringently adherent to the laws, tenets, and doctrines of the Christian faith (not limited to Catholicism) than is taught or required by the papacy or Christianity as a whole. Usually used hyperbolically as a negative or mocking criticism of someone as being overly pious. I can't believe we're not allowed to eat meat on Fridays while we're staying with Grandma. She could outpope the Pope! The zealous preacher-turned-Senator's campaign is so strictly rooted in Biblical law that many feel he's outpoping the Pope.

2. By extension, to be more extreme in one's behavior, attitudes, practices, etc., than that of the prevailing authority or standard of normalcy. Among the Nordic countries, all well known for their social welfare, Denmark outpopes the Pope in terms of providing care for its people.