As Citabria said, Combat Theater limits planes available to sides. Wouldn't like to have to switch sides to get fav rides in MA.
However, to spice up MA, what would happen if there were more sides? WWII often had more than three nations engaged in the same battle.
Chess motif could add three countries: Kings, Queens, Pawns. Lots of dry humor involved in all those. Pawns could be like The Mouse That Roared. Queens? More like Rocky Horror Picture Show. Kings? A plethora of Robert Shaw (the actor, not the air combat author).
Would victory and map changes be quicker or slower with six sides? Might be fun to try a week or so and see what happens.