On the Silverfin
I have a Boslic, Chandir, Ellora and Suliban serving onboard in 2378--species that don't appear to have any ties to Starfleet.
Plus you have all the species we've glimpsed on screen but which have never been named. The NuTrek movies are actually good for this: non-canon sources have the skinny Kelvin
alien was from the planet Monchezke; then there is also the big-eyed Kelvin
doctor; the bald, bug-eyed cadet; the bronze-skinned Enterprise
science officer; and of course Keenser.