I think you should get one free capital (your starter) and thereafter you can build new capitals in new star systems, but they may have a chance of rebeling and joining other empires (or starting their own) if they feel you aren't spending enough attention/resources on them. For example, once you build a new system capital, it can come up with missions for you to do, and if you don't do those missions, they lose a bit of loyalty.
Missions would be predominantly development and defense missions. EG. Marsicus 5 is worried about the pirates in their system, they're demanding a 300 point value fleet be stationed there within 2 minutes for the next 10 minutes following, or that you destroy the in system pirate base, otherwise they'll cease shipments of Crystals and cease development of all empire related projects in order to develop their own defense system, the Empire be damned!
Or, Halbadon is an out of the way asteroid mining area, but they're on the border with the nearest Vasari empire, and are concerned about their position, they are petitioning you to improve relations with the Vasari otherwise they'll go independent in order to maintain the peace.
Internal politics would be interesting to balance gaeplay.