Flocculencio
Donor
The Habsburgs united Austria, Spain, and the Netherlands in a simple way: marrying heiresses. So to get an Asian equivalent, you just need matrilineal inheritance accepted as a possibility. The difficulty here is that it doesn't seem likely that dynasties will go for matrilineal inheritance when a just-as-related patrilineal inheritance is a possibility, and (dramatically generalizing here, I know) I think the typical Asian ruler, not constrained by Christian rules of monogamy, would have an easier time producing a son. Asia's a big place, though, and it's not absurd that some part of it would develop traditions that limit rulers' legitimate male heirs. I think such a practice, though, is a helpful substrate for Habsburg-style dynastic unions.
Again, I'm not sure how that's any different from the Mughals or Mauryas uniting Bihar, Orissa and Bengal by achieving overlordship of them.
Like I said in my earlier post, people seem to be ignoring the fact that plenty of Asian empires did what the Hapsburgs have done (going by kasumi's earlier statement that he was looking for an Asian empire that ruled over multiple nations at once). Bihar, Orissa and Bengal are just as disparate culturally and ethnically as Spain, the Netherlands and Austria.
If you want it done in the same way the Hapsburgs did (i.e. through dynastic inheritance politics) which is not what the OP stated, things are a bit harder since Europe's dynastic customs were very different from Asian ones.