Is there a timeframe involved? For example, ACW to WW2 but not modern?
The sequel/prequel to
Aggressors: Ancient Rome is multiplayer (...um,
Imperiums: Greek Somethingorother? I'm not where I can check at the moment), and it has an overtly balanced multiplayer setup on random maps with minimal starting forces.
Field of Glory: Empires can be set up pretty balanced for multiplayer, in a nice asynch engine for up to 40 players (though probably not balanced in that case

), depending on what factions you choose. You can have teams or pure competition, too, although that can't be setup in advance before launching the game. (Players just ally themselves asap within the game.) The DLC expansion kicks back to the Persian Empire's rise, which is definitely NOT balanced but again it depends on where you and your fellow players faction-in.
Warhammer40K: Gladius can't be played asynch, only live (despite being turn-based -- the devs keep promising asynch is in the works), but it has a good balance among the factions, and again players can team or compete as they wish.
WH40K: Regicide can be played like straight chess, or as a tactical Marines vs Orks fight with chess rules overlaid, which is pretty neat. Naturally it's balanced like chess, though in the tactical ("Regicide") mode there are some differences in abilities. I can't recall if it's asynch.
For something closer to ACW, and asynch-capable,
1775: Rebellion works okay in its Steam adaptation. Can't be played 4p like the boardgame, though.
For something in the WW2 timeframe, the
Decisive Campaigns series pull off very well-balanced scenarios despite the real-life operations being hugely imbalanced. DC1 is overtly capable of being played by up to 9 people, and it's probably possible to play the others more than 2p with some shuffling around of the save games until 'turn-end'.