I just came up with a really inconvenient, possibly unplayable four-player game: The Evil Advisor
All you need is a completely normal chess board and a deck of cards that you can somehow divide into an even amount of cards that mean "yes" or "no". Out of the four players, only two need to know how to play chess - those play the role of advisor. The other two play as rulers. At the start of the game, both advisors pull a random card from the deck, which dictates whether their goal is to win the game, or lose it. They keep their respective card, showing it to nobody else.
The rulers, who ultimately choose where to move the pieces, always aim to win the chess game, and also know that the advisor may or may not be on their side, and don't know whether to trust the advisor or not.
If the ruler wins the chess game, they win the whole game. An advisor only wins if they reach their own goal - if an advisor's goal was to lose, but the ruler wins, the advisor loses, and vice versa.