Maybe the League has all of these? A race almost on the level of the Metrons, Patrons who in essence founded the League then started to withdraw from "normal" life (perhaps watching over a "cousin" species who haven't advanced as far?)--a anarchistic civilization with little resembling a government--a collective Hive without individuals at all--a race of carrion-eaters--another race who are very religious--a warrior race who make the Jem'Hadar look like girl scouts, etc. Perhaps a genuine respect for the Patrons unites them, but the Patrons themselves hardly ever interfere.
One can see lots of Federation citizens and Starfleet officers kinda freaking over meeting anyone from this League. They'd see another polity along the lines of the Dominion or the Xindi.