I would never plug in, say two monoblock amps, into two separate circuits. Your whole system should not tax a 20 amp circuit so don’t spread your interconnected equipment across them. At a minimum, you could introduce ground loops.
I took my two VTL Deluxe 300 amps to a stereo shop to audition a pair of Magnepan speakers. I wanted to hear how my VTL amps worked with them. The store plugged each into a different circuit in the room. The amps went into oscillation. Cripes!!! Plugging both into the same circuit resulted in stability.
Now to be fair, VTL did not make great stable amps. I know this because of issues I had in Center City Philly when we would have voltage sags (brown outs). But still, this should not have happened in this high-end stereo store. The owner did not know why it happened, but we assumed each circuit had differing loads on them from other equipment plugged into them.
In short, I don’t see the value in plugging in equipment that is interconnected across circuits. I think you are asking for trouble.
I wired both my previous and now my current home with a single dedicated 20amp cuircuit with a quad outlet. ALL of my interconnected equipment is wired to that one quad outlet. Same for my home theater… to another dedicated 20 amp, quad outlet.
Just calculate your draw and you will see it does not add up close to taxing a 20 amp circuit.
So… really you just need one dedicated circuit for your interconnected audio equipment. Other circuits are for auxiliary use such as lights and such.
Bruce in Philly