Everything about executive control, every single time. It starts out with "we need clan comms, tags, decals" then a few pages in this idea of asset ownage, shared assets and the usual garbage gets added. Garbage, mind you, from my point of view. Player named minor factions, not a problem. Same players guiding said minor faction through manipulating the BSG? Bring it on!
Players owning assets that only governments can afford? Hell no. Players owning planetary systems? Again, hell no. The Federation can own planetary systems. A government with multiple tens of thousand subjects can own a planetary system. Not a group of x hundred pilots.
If you meant that the guild would use the current game assets (powerplay, board missions, CZs etc) to expand a chosen minor faction, then yes. If you mean that the guild would get direct control over a minor faction and decide where it moves, what it does, then no.
"Ownership" is a squishy term in ED. (Oh, har har. Pun unintended)
The station is "owned" by the minor faction, but it is just the economy, trade, duties, etc.
The station itself is like an Oasis, or a Church in Medieval Europe. Once inside the bounds, the government cannot touch you. Nuetral ground.
Then there is security OUTSIDE, controlling access. They don't "own" the system or event provide a huge amount of restriction. Just too hard.
Then there is system ownership, aka, Power Play. There, local system forces, Power Play agents, and the Major faction like Fed Navy provide "security"
Systems are huge, so it is a wet paper bag worth of control.
So really, "ownership" would just be acting like the local station manager.
It poses an interesting idea for a mini-game, "running the station" and setting priorities for the missions available depending on the priority you set.