Mongols vs Cav/elephants/cannons

Hey guys!

This question is about Post-Imperial Age only. I play with a mate and we should be able to trade.

I've played Mongols in some recent matches and against infantry their mangudai/onager combo is just awesome.

But how do i play against Cav/elephants with lots of hp and potential to push into my onagers? I've tried pikes and they do well, but obv. miss the last upgrade and also drain a lot of wood.

The cannons kill my onagers. I can send light cav, but they are very easy to kill and especially in close combat can't get through. Sacrificing Mangudais also seems like a bad trade. How do you guys manage this?

Thank you in advance!