What is needed to play X-wing with 4 players?
The game is structured such that there are shared turn phases.  Everyone's moves happen in a single phase and the order is determined by model statistics.  Then everyone's shooting happens in a single phase and the order is determined by model statistics.  You can basically add as many people to that system as you like and they just take their actions in order based on their model's stats.

To play in two teams of two all you need is to own enough models so that each team member has enough to control that the game is interesting.

To play in a free-for-all with more than two players the only house rule required would be determining the tie-breaker for who goes first when two models have tied statistics.  (In the two player game it is always Imperials have the initiative if all other checks are tied, so if there are "imperial" players who are enemies you need a system to break the tie.)