The fighting bodies of Terrun that stand outside any one crown's army: orders sworn to hunt or cage demons, the licensed and unlicensed hunters of Hollows, and the companies that sell their swords. The armies of states are with their governments, such as the Proturan Military and the Sancturi Military.
The Shrine Knights: cheap Kalari witch and hollow slayers funded by temple collections.
The White Fire, the secret society whose members lead the Valyr, is with the arcane orders; the Imperium's own devil and Hollow slayers, the Dae'Venari, are with the factions of the Sancturi Imperium; the Keepers of Valnyr are a government.