The Inter-Stellar Concordium, portrayed in Starfleet Command II
(to include the Orion Pirates standalone expansion) is a multi-species union, based on the original version
seen in the Star Fleet Universe. (Taldren made a couple of changes to their take on the ISC, such as adding in the Meskeen, an amphibious species that does not exist in ADB's version.)
The SFU has a few other multi-species realms, which have yet to show up in a SFC
-esque "hybrid" game setting; such as the WYN Star Cluster (a collection of renegades and exiles from various neighbouring empires), the Męsron Alliance (a multi-species union founded over in the Omega Octant of the galaxy) and the Federal Republic of Aurora (another Omega power, this one established by various "lost colonies" transplanted from Federation, Klingon, and ISC space). There is also the Imperium, a multi-species power out in the Triangulum Galaxy, but it's not yet clear whether that realm is dominated by a single species or not.
So far as Paramount/CBS novels go, I remeber there being a power called the Regnancy of the Carnelian Throne present in The Buried Age
. I'm not sure off-hand if they had a primary species "in charge", of if they treated each of their member/slave species equally.