Maybe a Rome game based more on factionalism in Rome, similar to The Republic expansion, each player controls a faction in Rome (I think Total War did this too), and struggles to get two consuls from their faction, which gives a lot more options.
Political simulator ala Republic of Rome(Avalon Hill boardgame).
Dynasty simulator as you marry into other senatorial families to pull them to your faction.
War simulator, when the Republic declares war (often something you have no control over), you lead armies to war. But in peacetime, if your faction isn't in command of a unit or your faction is a consul, you don't get to move armies at all.
Just some random thoughts.
HOI hasn't had any updates in a long time. Its due too. I'd like to see a HOI simulator with a deeper economic model, not quite as deep as Gary Grisby's War in Russia, but it would be cool to get a bit deeper. Maybe drop "infrastructure", and have actual rail lines and roads. maybe drop "Factories", and have "Rubber Factory", "Ball-Bearings Factory", "Engine Factory-Light", etc.
It would be cool if the advanced economic model was a toggle, so players could opt for a simpler experience with a checkbox at game launch.