I think this should work, if and only if it applies to large bases. We'd obviously need more large base options, but the general idea is there.
After buying a large base like the vault, you have one week IRL to set up your defenses/whatever you need to get your base together. After that time, the location becomes visible when the player gets near it (possibly with some kind of ODM roll to make it less of a guarantee and force players to search the area), and disappears once they are a specific distance away. (Let's say that these bases are pretty well hidden and just a general idea of where it is doesn't guarantee you'll find it again.) This way, larger factions can actually promote trade and things like that at their base, but also allow for faction wars.
To prevent absolute raiding of the bases, each can have a room or two that needs a key (or an extremely high lockpick skill). This way, if your base is being raided, you can run away with the key, and hope your valuables remain untouched.
On the WM, the name of the faction would appear over the base, just like cities have, and the faction can edit the message under the name to whatever they like. It could be anything from 'open for trade' or 'recruiting new members' to things like 'trespassers will be shot on sight'. Unnecessarily offensive messages could be removed, and on repeated offenses the faction would lose the privilege of editing the message.
This system would also require some kind of member limit on bases. Let's say a cave could have 15, a medium sized base could have 30, and a large base could have 60 (there could possibly be locked areas of the base like a staircase behind a locked door which, after unlocked through some challenge/quest, would allow for a few more members and give the base a little more space). This way, the faction would have to limit the number of alts added into the computer, and would also force larger factions to buy large bases and subject themselves to this system. Base upgrading/buying multiple bases with one faction name would probably be needed here.
In order to support this, some type of militia system would be needed as well, which could work several ways. It could be that you get a recruiter NPC with your base who works the same way as the guy that gives you militia in an unguarded town (We could say you get one for free every 2 ingame days, and the others cost you money or other resources). You would have x number of slots for militia, but you could replace some with stronger mercs and slaves (maybe even turrets and robots, but that might be going too far). To prevent abuse, mercs/slaves would have to log off when you do (which may or may not be the case, I'm really not sure).