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3P/4Ptalia has no basis in canon, but it's based off of the 2Ptalia AU (2P stands for 2nd player). Needless to say, 3P stands for 3rd player and 4P is 4th player. 3P and 4P was added in-fandom because it would be inspired by not only 2P, but the 4 players option that often comes with gaming systems. tl;dr They're based off of 2P and the 4 players thing on gaming consoles.