Or maybe make it a single race empire?
Like: you are Terrans, all aliens are hostile/weird/not to be negotiated with.
You start with the single planet in the center then automatic colonization starts. There are two kinds of colonization: "official" done by corporations with the intent to stay in the empire, always nearby planets and "private" with the intent to set a far, far away frontier planet your independent home with own government.
So you are all the same race, just the population pararerly colonizes inside the empire and outside of it.
Then the population migrates as they see fit (you have no/low control over it).
Fauna & flora - instead of the "40 random races" there could be randomly generated fauna & flora on planets, some very hostile/dangerous. The thing is once someone colonizes the planet the fauna can travel too (there are always some idiots that take take their pet Xenozaur to another planet) and you some times don't want these to spread around.
Since you have no control over neutral planets it might become a breeding ground for these nasty parasites/diseases and you might want to introduce a ban/restriction to travel to planets outside your empire (or quarantine them, or simply bombard from the orbit as the last resort).
Hmmm, it might be interesting too I suppose...