In Dungeons & Dragons, you get to choose a number of Feats (one of which might give you +1 Charisma and another of which may allow you to disarm, and so forth), but there are also a number of Feats that come with one's race (extra skill points for Humans, resistance to magical attacks for Drow, different levels of low-light vision for different species, et cetera). Maybe if you graded the different race-specific Feats for different species in Star Trek Online (brak'lul for Klingons, über-everything for Vulcans, et cetera), somebody who wants to play a half-something-half-something-else could receive a certain amount of Racial Feat Points at character creation, and get to choose from their two species' Racial Feat pool? I'm thinking that the amount of Racial Feat Points they'd get to allocate would be slightly less than the value of a full-blood's full set of Racial Feats; that's the price you have to pay for this extra level of customization.
Now, I'm thinking that even if there are species-specific starting points (such as Qo'noS for Klingons, Vulcan for Vulcans, et cetera), half-bloods would all start at Starfleet Academy, because let's face it: Everybody in the Universe ain't too keen on cross-species breeding (for instance, I can imagine many Klingons feel it is a disgrace to dilute the blood of warriors with that of off-worlders).
Indeed, in dealing with factions and other such aspects of gameplay, I figure they'd probably be treated similar to Humans, who have always been the most multi-cultural species in Star Trek (and in many other franchises, too).