I can see a few candidates from Asia:
From the Indochina Pennisula, either the Khmer, Champa, or Vietnam, as even though all three were significant empires there's really no need to add more than one of those three.
From Indonesia, the Majapahit or Srivijaya (again don't need both)
From Central Asia, the Timurids and/or the Khazars
From South Asia-East Asia, Tibet
And if you want to include the Near East:
The ancient Fertile crescent can use some more representation, so either Sumer, Akkad, or Assyria, and I wouldn't mind the Hittites (Anatolia)
Each of those groups are distinct enough from each other while still being historically important to warrant inclusion.