Some sort of evil psionic-type civ, maybe. So the reason the leader gets more and more is that he absorbs the minds of others and add their knowledge and power to his/her own. It could work with souls too. Could be an undead leader, or demonic, or just someone who meddles in dreadful and eldritch knowledge Man Wasn't Meant to Know Of!
If evil isn't wanted (*grumble*), it could be a neutral leader who have access to some sort of device or ritual that increases his power. But that's not as cool as a soulsucking braineater![]()
It might be cool to introduce an extra late game civ. Why not bring in an evil psionic civ immediately when Pass Through the Ether is first researched? Civ would prefer to appear on empty territory, is also Barbarian friendly, and if no free territory is available, take over the smallest non-island city of the largest civ (without a wonder or holy city).