In Master of Orion II you could create multiple custom races and then choose to play one of them against the others, or all of them against the computer by yourself, or add any number of players in between. For example you and a friend could each have four races against the other. or one race each against 6 AI controlled empires. I would very much like to see something like that. Trading technologies back and forth and having races that specialized (instead of cities) in different fields, i.e. a race of +2 scientists trading population with a race of +2 food or industry.
This could also be done in Birthright: Gorgon's Alliance - Advanced Dungeons and Dragons. You could create roads and trade routes and send gifts of gold to allies, allowing them to make last minute armies to battle the AI controlled armies at borders and prevent them from harming either race/team/player.
M.A.X. Mechanized Assault and eXploration had hotseat. this was ages ago, but my dad and I had a lot of fun duking it out.
- I plan to re-install Civilization: Call to Power pretty soon, but I think I remember playing more then one team in this game as well. [note: my laptop was virusassinated and I don't currently have a pc that can run E:WoM or I'd be playing it instead)