A Parasite Faction

The parasite faction would take over the bodies of other species. Units of population they control have the same FIDSI stats as the base species, but the political views would correlate to the parasites. Because of the physiological changes their parasitization causes in the host organism, pop growth occurs much more slowly than other factions; while they can grow their faction and colonize other systems in the normal manner, this won't really be feasible until late-game techs ease the growth problem. Instead, they will need to send out infestor ships to target already-colonized systems. The nature of the parasites could be kept secret from other factions, and trade routes could act to spread the parasites passively as well, encouraging a diplomatic style of play as an alternate path to direct infestation.

By default, they would be unable to parasitize inorganic species, but technological advances could open up new avenues for them to assimilate the galaxy. They could live on any colonized planets based on the tech of the host species, but will still need to research the appropriate techs if they wish to establish their own colonies; infesting an otherwise uncolonizable planet gives a bonus to the research for the corresponding tech. 

Other factions will need access to techs that can help them defend against infestation. There could be diplomatic penalties for the parasite faction once their nature is discovered by another faction.

The parasites have their own ships, as normal, but will have access to improved tech to allow them to seize opponents' ships mid-battle, enabling them to pursue a military strategy involving seizing enemy fleets as they progress. Ground invasions will be possible, but due to low population and manpower growth, infestation will be incentivized.