There are never (or at least very nearly never) more than two sides in a war. This realization didn't come to me by looking through history, or by looking at a theory-it came to me while playing Age of Empires II, a real time war game, online. Almost every game created is 4 vs 4, 3 vs 3, or some other variation of one side versus the other. Black and white, two sides, no third party interfering.
The reason why that is the common preference is simple: it's easier. Third parties are simply a pain, because suddenly another variable is added to the equation. Now, not only do you have to maneuver your troops against an enemy, deal with your economy, and work with your allies, but now you also have to engage in diplomacy with an active enemy so that they attack someone other than you. It also makes it a pain to actually 'win' that said war: everytime you become the most powerful entity you suddenly come under attack by the other two parties.
This being said there has never existed a true three sided war. World War II admittedly came close, as the Allies, USSR, and Axis each had separate agendas, but the USSR solely fought the Axis (though this could partially be because their position was locked between Germany and Japan, so attacking the Allies would have been difficult even if they wanted to). Try to think of a different war that presents three equal sides all actively opposing each other, and you will fail. Peter Mair, a political scientist states that "there are no three party systems; there are no unbalanced two and a half party systems" (310). A two and a half party system is described as a system where two major parties exist with a lesser third party (like the independents in America). This third party cannot win itself, but can generally determine who does win if they work solely against one of the other parties.
However Mair's statement that there are no true three party systems is most significant. It demonstrates that not only are there never three equal parties in a war, but also in politics. Truly the only place were three equal, opposing sides seem to sometimes exist is in games. And when it does it isn't pretty. Generally three opposing, equal sides leads to games that drag on for hours because all the players are too scared to tip the balance of power in any direction, since shifting the balance could hurt them no matter what. If power shifts away from them, they are weaker. If power shifts to them, they could be perceived as a dangerous threat and be ganged up on until they have lost a significant amount of power. No one tips the balance, and it goes on forever (a scenario actually presented in George Orwell's 1984, interestingly enough).
Thankfully this doesn't happen in the real world though, because it could potentially lead to a never ending war.
Orwell, George. 1984
Microsoft. Age of Empires
Mair, Peter. The West European Party System