Break before Make means that the first circuit is disconnected before the second circuit is engaged. This seems logical, but with some switches there could be a brief period, really a tiny period of time, when both circuits are engaged. You do NOT want to have two amps on line at the same time.
A typical 1 into 2 (1 amp, 2 speakers) or 1 into 3 or 1 into 4 speaker switch could work backwards, as in 2 into 1, that is 2 amps into 1 set of speakers. But we would have to know what was in the Speaker Switch. Many have passive circuits inside to balance the impedance of multiple speakers. I'm not sure how that would work.
If you can find a pure switch and if you get a 1 into 3 switch then you could potentially connect amps to Switch 1 and Switch 3, leaving the middle Switch 2 unused to assure no possible connection of both amps at the same time.
In this case, I would prefer a switch with a rotary dial rather than push buttons. The rotary switch dial assure that the center position is a disconnect. Though Push-on/Push-off button switches could also be used. You just need to make sure that there are never two ON at the same time.
I also confess that I'm having a hard time finding a switch with a Rotary dial, though I have seen them in the past.
You could even put some small Power Resistors on the middle Switch 2, to assure a stable load on the amp while you switch.
However, that said, the Beresford TC-7220 is specifically make for switching TWO Amps and up to Two sets of speakers. However, while it would probably be OK to not do so, I believe the Beresford, as is likely for any switch, it is recommended that the Amps be OFF when you switch them.
I'm not sure how necessary that is, it may be just an extra safety precaution, but I vaguely remember that being discussed as a requirement.
Also, since you have two amps, and we assume one set of speakers, have you considered Bi-Amping. One amp driving the Mid/High section, the other amp driving the Bass section. If your speakers have FOUR speaker terminals on the back, then they can probably be Bi-Amped. Though you must make sure you REMOVE the Jumper Bar between the speaker terminals.
Just a few thoughts.
Steve/bluewizard