I don't think we've seen any of the member spieces with any other spieces on their crews (with the exception of half-human Sela).
And that was something that always bugged me. The Klingons, Romulans, etc. are called "empires." An empire is a state in which one culture rules over multiple other cultures and draws on their wealth, resources, and labor to sustain its needs. That almost invariably involves using them in the military, whether it's the Romans using Gauls and Greeks, the Ottomans using Janissaries, or the British using Indian and African troops in the World Wars. Not only does the metropolis (the ruling society within the empire) need the personnel to maintain a large enough military force, but using the subject peoples as cannon fodder spares the dominant culture from having to throw as many of its lives away.
So it never made sense that these so-called "empires" in ST were monoracial, that we never saw their subject peoples serving on their ships. That's one of the reasons I like
Nemesis -- its introduction of the Remans, a subject race used as cannon fodder, made the Romulan Star Empire actually start to feel like an
empire for the first time ever.
In the books, we've occasionally seen the Klingons portrayed with subject races aboard their ships --
kuve in John M. Ford's version of the Klingons,
jeghpuwi' in the modern book continuity. However, they're treated as mere servants rather than soldiers, which makes it a little less plausible.
Before ENT explained the Klingon forehead issue once and for all, I was leaning toward the idea that maybe the various different-looking groups called Klingons (TOS smooth-headed Klingons, TMP single-spine Klingons, TSFS/TNG bony-plate Klingons, TUC pink-blooded/finer-ridged Klingons) were actually multiple species or subspecies, that "Klingon" was perhaps the name of a nation rather than a race. That would've made them feel more like an actual Empire. Alas, it was not to be.