It sounds like you have a stereo cab; meaning you have the option to run each speaker separate at 8 ohms each or run them together in series at 16 ohms total.
The problem you're going to run into in what you're wanting to do is an ohms mismatch unless you move cables around. Typical ABY pedals are not built to handle signal flowing between the amp and cab. You'd fry your transformers trying to use one of those. What you need to look at is a head/cab switcher. There's still an issue there. Most head/cab switchers that allow for extension speakers will run them in parallel which would give you 4 ohms. So you're still dealing with an ohm mismatch.
You would need to add some sort of impedance matching device in the chain like a Zmatch transformer or similar. You wouldn't have to move cables around, but the setup may get complicated depending on the units used. You may also still have to keep track of which speakers were active and manually switch to the correct impedance on that side of the chain. Plus you're getting into an area where the setup may not be worth the money for what you want to do.
KHE looks to offer the simplest setup in this way. Use any of their amp/cab switchers combined with their ZMX-1 impedance matcher. You're looking about about $1700 for the cheapest setup.
The next step down the line is an all in one unit. The only two that come to mind are the Fryette ZMACS 4x4 and DeLisle 4x4 Pro Plus with built in attenuator. Both would allow you do what you are wanting without having to worry about impedance matching in an all in one setup. Both have space for 4 heads and 4 cabs(speakers). Like the KHE they wouldn't be cheap either.
Differences are function and price.
The Delisle has a built in attenuator, uses rotary switches, and costs $1500
The Fryette is push button, but can switch everything via programable MIDI, no attenuator, and costs $1000. I don't think a MIDI footswitch is included.
I generally recommend DeLisle since I own several of their switcher and can attest to their high quality. KHE and Fryette are high quality as well, but I've never used them myself.
https://www.khe-audioelectronics.com/shop-1
https://www.fryette.com/zmacs-4x4/
https://delisleguitar.com/shop/de-lisle-amp-speaker-selector-4x4-pro-plus-with-reactive-attenuator/