This is a fairly strange request, as it's pretty simple to just cram all the hardware for the second rig into a second case. You certainly can't share hardware between two computers living in the same case, so I don't know why you'd want to do this.
Usually, people are looking to do the opposite. They have one set of peripherals (mouse, keyboard, monitors) and want to connect two computers to them. This is accomplished via a KVM switch, which can be had at a variety of price points from pretty much any retailer that sells that kind of thing.