You can have as many amps and cabs as you want. You can also have as many cabs off one amp as you want. But never have more than one amp powering a given cabinet at a time.
You do get some players who actually switch between different amps throughout a gig, but that's not too common. More common is to have a single preamp sending a signal to multiple power amps, which each push their own designated cabs. In that sort of setup, all you're doing is either running the preamp-out into a splitter cable that connects to the input of each power amp. Or, into the first power amp, which has an pass-through to an output that can be connected to the next power amp in line.
If you use an ABY switch, it needs to be one that disconnects the first set of contacts before engaging the other set of contacts. "Break-before-make" is the term often used for that.