While I really do appreciate your obvious answer... a KVM is one set of keyboard mouse and video for two CPUs. I searched for "double" or "dual" KVMs extensively before I posted this question.

I'm looking for a way to switch between two sets of both without manually unplugging them all every time I want to switch.

I would have:
Monitor, Mouse, Keyboard - SET A
Monitor, Mouse, Keyboard - SET B
CPU - Y
CPU - Z

Most of the time, SET A is connected to CPU Y, while SET B is connected to CPU Z, but when I flip a switch, SET B is connected to CPU Y while SET A is connected to CPU Z.

If there is a way to accomplish this with a KVM, I'd really appreciate more than a one word explanation. Because I'm just not seeing it.