Looking for Power amplifiers with built in A/B speaker switches

In my experience, speaker switching is a bottleneck to an amp's design. Use a 2nd power amp for the 2nd set of speakers. 

Given your budget, I would move forward with the Accuphase P-4600. Hard to beat with its build quality and features. I also run a Coda amp as my primary, the Coda S5.5. The only Accuphase I have is an old P-300V built in 1988. The P300V also has the dual speaker posts with front panel selector as well as dual input with front selector. I will put it in service for speaker comparisons on occasion or just for a change of pace. I also have a switch box, but prefer not to use it unless I really want to hear the Coda only. In terms of build quality, the P300V was serviced by Accuphase in 2020, over 30 years of use before needing servicing and everything inside is solid and over engineered. The Coda as a high biased Class A vs. the P300V Class AB, they do not sound the same but they are both enjoyable. I only bring this up to say that the modern Accuphase amps have only improved over the years from what I have read.

Good luck!

everything I see/read about Accuphase is impressive, here’s a used P-360, two sets of speakers, 300 wpc 4 ohms, 100v model

https://www.ebay.com/itm/236484826810?itmmeta=01KBZSRFHSJENSR2FNF5BGTZWY&hash=item370f9816ba:g:heQAAeSw7CdpIos-

I think T+A has that function.

Yamaha M5000, $10,000, about 5k under your budget

It is a very refined power amp (not integrated), a very nice piece....ideally designed to be paired with their c5000 preamp....but, also works on its own. I use it to do the  easy swap a/b between some speakers i have. Imo, it was designed for those musicians with the golden ears, but, it could also work for the hifi enthusiast, gear head, music lover, whatever they feel they are...