One of the things i really liked in Stellaris was the endgame crisis (basically random quest events that could bring the end of most empire if they didn't work together against it [IA rebellion, "zerg attack" extradimensional beings).

We already had some kind of common quest to all empires in late game in Endless legends and i think such thing can be interesting if well done (it can give you a new challenge if you are dominating your enemies too hard and it can give you opportunities if you are not).

Also they also had (with a dlc) a "space leviathan" concept) (basically space is a big place you never know what you may find, like from a planetoid ship to a space drake and all that's in between) you could find them early on but couldn't do a thing until you had advanced enough and that made exploring systems much more fun and rewarding (i would really see such things in a few hidden systems that don't belong in any constellation, that way they wouldn't hinder normal gameplay and would be a bit harder to find which would fit their role as hard to find hard to kill but rewarding quests).