If you tie the player/faction bases to the BGS then one of the key things you build in is that time needs to be spent in their defence. Whilst a player base is below a certain size I would advocate it is hidden from the BGS and cannot change ownership. However any player can visit those facilities and take advantage of the services. Once a base becomes a certain size or is created by a player faction then it is subject to the BGS and can change ownership.
For a faction even if they were allowed more than one faction base, those faction bases need to be defended. Whatever mechanism that involves means that part of the faction activity needs to focus on defence. Even more importantly in faction conflicts the player faction base should become strategically important which will mean that factions will need to focus attention on them. This should have the purpose of focusing factions on each other rather than individual players. If faction expansion can only happen in systems immediately adjacent to ones you already control, then activities to take over bases can only happen between factions controlling or occupying adjacent systems. Players not belonging to player factions present in adjacent systems should have free travel to and from these stations.
For a faction even if they were allowed more than one faction base, those faction bases need to be defended. Whatever mechanism that involves means that part of the faction activity needs to focus on defence. Even more importantly in faction conflicts the player faction base should become strategically important which will mean that factions will need to focus attention on them. This should have the purpose of focusing factions on each other rather than individual players. If faction expansion can only happen in systems immediately adjacent to ones you already control, then activities to take over bases can only happen between factions controlling or occupying adjacent systems. Players not belonging to player factions present in adjacent systems should have free travel to and from these stations.