If you know the name of the chess variant I'm trying to describe, please leave it in the comments.
My friend and I have concieved an (most likely already thought up, nevertheless very fun) idea of chess where 2 moves take place at a time. The main rule we have that concerns checkmating in this variant is that you can move through check so long as you don't end up in check at the end of the second move. (This also means you can move another piece before getting your king out of check)
How would one checkmate in this situation? An even situation would be optimal for the response, I know how one could checkmate with an inordinate amount of pieces.