Perhaps religion could be used to represent political organisation?

We have 7 slots, which is more than enough.

You could have a number of systems represented:

Democracy (Certain Greek States)

Tribal (many babarian settlements and factions, early Pahlav)

Monarchic (Diadochi, perhaps Averni, late Rome)

Republic (Republican Rome)

Commercial Oligarchy (Carthage, maybe settlements like Rhodes)

Theocratic (no actual factions, but present in Egypt and maybe India)

Each faction could have a starting "religion" (=politcal organistation) but this could change: Rome was rent later in our period by oligarchic, democratic and monarchic tendencies. The Koinon Hellenion faction woukld be rent from the start by Oligarchic/Democractic clashes

There would be buildings that gave a conversion bonus to a particular system: tribal assembly gives 5% to tribal, tribal confederation gives 10% etc.

Theocratic cities could start with a "temple administration" building giving a huge happiness bonus to offset the religion penalty, but a massive conversion bionus: Egypt was notorious impervious to outside influences until the advent of christianity. however if you want to "politically convert" that population by destroying the theocracy then you will undergo massive upheaval.

Other buildings could skew a settlment toward a political inclination. Eg a stable building could give a 5% conversion rate to oligarchy: if you have equites, they get organised politically. A "grain dole" building might tend to democracy (as well as hapiness), as would a hoplite barracks (but not a phalanx training ground)

Camillan and Polybian barracks might give an oligarchic bonus, but Imperial barracks would give a monarchic bonus.

Certain buildings could give ancillaries witha political conversion bonus (demagogue, magistrate, tribal chief etc), faction leadership could give a conversion bonus etc.

I'm making this up as I go along, I'm guessing there's not enough buildings to make it work, but it occurs to me that its a way of getting some shades of political colour into the game. Gives a player a reason to massacre certain cities, whiuch was present historically (eg Alexander with Thebes, Rome with several enemies).