Mission to make one species the most powerful
What have you folks found is the most effective way to do this, particularly on larger maps? On smaller maps it's usually as easy as blowing up the planets of the competition, but that's an uphill battle on the larger maps, especially if they're the species ahead of them are heavily established - they recolonize faster than I can blow them up.
Supporting a species by questing for them helps to a limited degree but it can be slow going. I'm thinking a combination of that and starting/supporting rebellions to splinter the leading species into smaller factions is the way to go but haven't tried it yet.