Please, please stay away from the ahistorical stuff. Part of the attraction of the game is the reasonable amount of accuracy it has. I would enjoy a meta-game with inter-/intra-faction intrigue and management. Add a happy/unhappy scale to the drivers, and allow the team and faction to fund events that would please a driver, or a group of them. Parties, etc. Put in the occasional opportunity to have the player be bribed to do something, and paid if he does - for example, 250D to stay behind a particular driver for the first two laps, or to attack a particular driver. Fail and you might be beaten, adding injury and unhappiness; succeed, and you could rise in the faction ranks. You should be able to (with a lot of cash) bribe someone to sicken an opposing driver or mess with their chariot or horses. Something like the current random events system but with agency. You might even be able to hire a free driver away from another team (and of course it could happen to you if you have any who have bought their way out.
It would be cool to be able to attract faction backers who would contribute money and morale support occasionally in return for a percentage of wins (and the returns from their bets), but who would pull their support if things start to go bad.
Also, it would be fun to see 1, 2 and 3 horse team races.
Of course, the biggest deal would be multiplayer. Best way to do that is timed turns, to prevent trolling other players. That would add a sense of urgency to the game too. A replay mode would be tons of fun, too.
BTW, Nukkxx, I'm 99% sure Roman law did not allow multiple wives. You probably would want to tally slaves, or mistresses or something.