Here's my clan/faction proposal:
Players can create clans for a LOT of money. Membership in that clan grants three things: Private chat channel, an in-game tag/guild abbreviation, and the ability to see other clan members within 100ly on the galaxy map.
Clan leaders/founders can ally the clan with one specific minor faction in the ED universe, and receive favorable trader status or better missions or some other fairly intangible benefits. Maybe reduced reload/repair/refuel costs, or a randomly generated rare commodity for faction members only. Whatever. Nothing major. Multiple clans could ally with the same minor faction, there's no reason it'd even have to be limited to one clan per faction. Clans would have to earn the new status level via normal ED game mechanics, where you run missions/turn in bounties/etc. and partial credit applies to your clan's ally status.
Any "control" of the universe comes via the standard, existing game mechanics of helping your clan's minor faction extend it's influence in neighboring systems. Nobody owns a space station, nobody "controls" space, but the mechanics are still there for territorial control of the precise same sort that already exists in-game.