I would like to own a small outpost too but seems unlikely. I guess that we could ask for player faction owned outposts... I know, we already have that, but I was thinking about the capability of squadrons to build new ones.
For example, if an expansion doesn't find a system in 30 lys around, it could look for not-habitated systems and would enter in some kind of "construction" state. Trading and recon missions would be spawned and if there is a success, an outpost is created in the empty system. If successful, another state is started like "colonization" and missions to transport colonizers and deliver materials are triggered. Depending on the success, the amount of starting population and services is determined.
From then, other factions could expand into that system, creating space for all the new player factions.