Theoretically the game can support hundreds of stars (with dozens of planetoids per star).
But it becomes impractical to manage such an empire.
But it could be... if you had a few simple options.

If, once a star has been conquered, selecting its sun should bring a "system" menu that allows you to do a few cools things. Like set an AI to auto upgrade / colonize / patrol / build / defend all the contents of the system.
Or to manually select options such as "Upgrade all planets" (one time payments) or template based fortification. (create templates for different planet types).

The coolest option should be massive structures or structures that are impractical in a warzone...
1. Option to build refineries on astroid belts (uncolonizeable) that would give refinery points, visual, and automaticall capture the astroids in that specific belts. The refinery has normal refinery health and provides no population or taxation, it is extremely vulnerable but makes sense in a controller star.
2. Build observation posts... very weak satellites orbiting gas giants OR sitting in the middle of nebulae.
3. Build warp gate around the sun. Extremely expensive item that allows warping a fleet (up to a certain size) to any other warp gate you own. If you warp to a system without a build warp gate (such as one that does not have any natural wormholes) then the wrapgate overloads and explodes (loosing a LOT of money... and I do mean a LOT... but allowing you to expand to otherwise isolated stars... it makes no sense for there to be completely isolated stars).

Maybe give a research bonus per every star system you control, that increases the more stars you control. And unlocks super research items (a whole new level of extremely expensive, extremely slow research, that deals with having an empire spanning several stars.)

The AI would try to defend against invaders (especially ones coming through wormholes) but you could step in and take over and do it right... It all depends on the strength of the specific star system.

Maybe have it build a "tug" capital ship (one per star) that could move stationary structures in a planet or place the structures that go on uninhabitable "planets" (like astroid belts).

If supply is determined by population then each star should have its own supply caps, and the AI could keep a nice garrison patrolling each star. (the size of which depends naturally depends on the population of that star).

A really neat thing would be if each star would have its own economy, and when it builds a warpgate at the sun it joins into the global economy.

This could tie back into the cost of the warpgate (and its destructabilty, either through warping to an uncontrolled system or through attack). It will be a difference between a steller and intersteller empire. Once a warp gate is down in a unified star (one without any hostiles) then it should automatically apply its income towards building a new one and joining the steller empire. (It should probably be build in units... allowing you to pour resources as they become available, instead of only starting construction when the full price is there... For example, require it to be built in 200 pieces costing 1000cred, 100 metal, 100 crystal each... or some such.