My Theories of what they could be structured like.
7 Seraphs:
There are seven deadly sins, so wouldn't there be seven heavenly acts as well? Like the highest is Martyrdom? Maybe there are Seven leaders, each represented by the Act? These guys are lawful good.
Eye of Osiris:
I see these guys like Watchers, as Osiris is the Egyptian god of the dead they are relatively passionless and have no real rivalries. They stay pretty neutral.
Dead Orbit:
They kill for the fun of it, to use the spoils to build their empire. Not Chaotic evil, but neutral or lawful evil.
The New Monarchy:
These guys are like a feudal society, based on bringing the strongest to the highest ranks. more neutral good they will kill who they need to to make their empire stronger but don't kill for fun.
Future War Cult:
Chaotic Evil they wage war on everyone, life is a constant struggle for them and only the strongest survives. Technology is like currency here.
So if you have any ideas PLEASE POST THEM!