Can I combine speaker cable minus from two different amps and only switch the plus to change between them?

It sounds like a weird thing to do, I know. The setup is like this: I have a computer with J.River Media Center feeding both a Yamaha receiver and a car amp running on a 12V psu to a set of speakers on the patio. When I use the speakers that are always there, a set of Polk Atrium 8, I run them on the car amp because there I have a high pass filter set so the bass won't distort. When we have a party I take out a pair of Wharfedale Titan 12" PA speakers made for troubadours and small bands, which can take a LOT more bass and a LOT more volume, so they run on the Yamha receiver (a ten year old top model with lots of power). There is are boxes outside with two relays, switching the speaker plus to either the Polk or the Whartedale pair, so they can never work at the same time. A switch sends 12V to the relays, switching between the terminals. The minus is always on for each speaker terminal.

The problem is switching inside. I could of course use four relays, one pair for each channel on plus and one pair for each channel on minus, but something tells me that's overkill, and that I only need to switch on plus and collect the minus from both amp's left and right channel to a common left and right minus to the speakers. They do have a common ground because the line in is fed to them both. Am I right? Am I even making sense?
 
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Even if the power amplifiers work in the normal single ended mode with common output ground, the method with only one speaker wire interrupted is tricky. It will almost certainly add hum/buzz/noise due to additional ground loops between the two amplifiers. A/B testing with two power amplifiers is not trivial. Also clicks and pops due to different output DC voltage of two amps is to be considered.
 
OK, thanks! I want to avoid ground loops, so I'll use relays for both minus and plus for the channels. The car amp is actually bridged, but not on those channels, it is bridged on a third channel that I plan to add a subwoofer to, when I get around to build a waterproof enclosure for the boat sub I have laying around.
 
Btw, an electronic question if anybody knows: I remembered I have a bunch of Omron MY4IN 250V relays with 12V switching left after previous projects (home automation before Z-Wave and 433 mHz, when I needed to switch relays to turn on and off lights and other stuff). They are four channel double throw relays, so one would take care of the whole business. The contact current is rated at 5A, as you can see here:

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Is that enough to stand the wattage from the speakers? The most powerful, Yamaha amp is rated at 140 wpc, but I have never used it on full blast, I think the neighbours on the other side of the fjord would probably call the police then... 😂 I have no idea how to calculate watts into amps with speakers, since I have no idea of the voltage.
 
@ejp, thank you! Cryptonite for me, I am totally hopeless with math. But I found a calculator for that, I didn't even know that was possible. If I am correct, this should work nicely:

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Btw here are the Wharfedale 12" PA speakers. Great for parties! Note the mirror image upper right of the Wharfedale E-series speakers that are part of my home theater/music setup. I have 16 of those in different sizes in my HT setup, with four Wharfedale active subs and four JBL (the outcasts of the setup) as height speakers in the ceiling! 😎

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