I am thinking maybe the Covenant can get an "ooze lair". This will permit members of the Covenant wanded for it to set up a base in the wilds away from their hub to raise their very own ooze and tell a unique story as to why. I imagine some benefits might be:
1) Free Rest
2) Ooze Themed Gear
Some other stuff. While the 'bases' for the covenant are great, there is little incentive to use them past level 7, unless I am completely missing my mark. You already get free resting as a member of the Covenant in the Fortress, and while being able to feed an ooze and get possible gear for it is great, I think it's limited in scope as to potential Rp possibilities.
I'd much like the idea of an ooze lair where you need to defend and raise your ooze from the beginning in order to accomplish certain covenant objectives.