I guess you could, in theory at least, daisey chain the amps but it's not something I'd want to do. The preference would definitely be for a tape loop switcher from the likes of QED (discontinued) etc.
Keep an eye out for the Niles TSB-3 unit. Two sold recently on USA €bay for approx. $40. I have one of their speaker and amp switches (four sets of speakers switchable and with independant volume controls plus switching for two amps) which is very well built and will probably outlast me!