If I make a mob farm on a another mob farm would that increase the spawning rates or would it not matter?

For this particular farm design, more layers do help efficiency, since it creates more areas for the mobs to spawn. Mobs spawn within 24-32 blocks away from the player, and outside of that range, they won't move. This particular farm design requires the mobs to be able to move.

This means that this particular farm design while resource efficient, only works with 1-3 layers, and relies on the mobs to move out of the spawning areas on their own.

There are other farms that are more efficient, since they force the spawning areas clear regularly. Like this one:

While it isn't resource efficient, it will increase the efficiency of your farm quite a lot.