How about something like this:
The center of the galaxy is filled with small minor civilized races (player starts there too), the outskirts of the galaxy are filled by 3-4 major civilized races and special/weird races. Minor races are agressive and unstable, these will be conquered by the player or by other major races (some will survive independent I suppose). Major races are more about keeping the status quo and significantly less aggressive.
Gameplay flow (standard game):
1. First the player will carve the Empire out of the neighbour central minor races, other major races will expand at the expense of minor races too
2. The player (Empire) start to interact with major races and there will be struggle for the borders, also primitive hostile races (Parasites, the Hive) will start to be a problem, probably rebels will start operating at that time too
3. The Empire conquered a significant part of the galaxy, major races acknowledged the Empire being the "top dog", now the goal is to protect the galaxy from the Annihilartors that enter via trans dimensional rifts, after they are dealt with all local races acknowledges you the Emperor of the whole galaxy (win)
Diplomacy - you might have an option to incite uprising of minor races that were conquered by major races.
Major races & culture - There could be 5 major races (civilized): Empire (player), Rodent Monarchy, Reptile Republic, Collective, League. They exert "culture" (Empire, Monarchy, Republic, Collective, League), minor races do not exert culture, they are affected by it. Now each planet will have these cultures and the point is, if you conquered a planet and its dominanat culture is Empire, it's all right, the local aliens will accept your rule. And if some other major race conquered a planet with dominant Empire culture, you might make them try to rebel in order to join you (Empire).
The balance here is that the Empire is the most desirable in the eyes of aliens (you basicly want the aliens to work, pay taxes and obey the Emperor and they can do whatever they like - you don't want to assimilate them like Collective or make them serfs like Monarchy, etc), so, if you invested in it sufficiently you should be winning the cultural/political game, military game being another thing (major races are strong and they started earlier).
I love those placeholder graphics, looking forward to seeing how this develops.
Note: Depending on screen most are the final ones at that point (but again that depends on the screen, there is a mix of placeholders and final ones).