With great power comes... a ton of weird crap that you are not prepared to deal with.
Phil Couslon, Agents Of S.H.I.E.L.D.
Making clan representation the standard limits possibilities, but it’s natural that a Prince would want to at least appear to be listening to all the clans. And it fits the mobster style to have meetings of the “heads” of the families. But of course, an individual Primogen might be a long way from the real power in a clan.
In Requiem, the informal leader of a clan in a domain is a Priscus, while Primogen are still the Prince’s advisors, so both positions exist at once. The Covenants have their leaders as well, to further add to the potential for multiple conflicting power blocs. This would be one way to go in Masquerade, not least as the clans tend to be more politically united there. Maybe clan leaders get together independent of the Prince’s coterie of advisors - maybe they’re the real power in the city, as in Chicago By Night 1.
Just about any power structure could emerge in a given domain. It could have an unbeatable ancient god-king, a coterie functioning (more or less) as a council with individual purviews to govern, a Sanctified or Crone theocracy even in Masquerade if you change a few names. Among other things, Damnation City has ten princes who would radically alter the feel of a city. (I’ve actually seen something like the Phantom, the unseen Nosferatu prince who rules through messengers, in New Bremen, before a more “traditional” Prince came in.)
A recent thread on the White Wolf forums had me thinking about the anarchs as it asked what they would want to put in place after bringing down a Prince. Just about anything except feudalism. So we have anarchist anarchs naturally, but also representative democracy anarchs, Socialist collective anarchs, totalitarian anarchs...
Imagine the next city along, a few hours away, being taken over by a cult of personality, and the PCs’ city sometimes took in runaways bringing reports of the dictator amassing an army of loyal vampire shock troops.
And what of characters who end up on or near the throne? How long before they have to make a decision that could knock down their Humanity, alienate an ally or start a revolt? Check out series two of the original Being Human for a perfect example of why you don’t want to be Prince.