Buzz or Noise in Distribution Amp Output

I have a multi-zone audio distribution system. Each output is 25w/ch and can support 8 or 4 ohm loads. In some rooms, I hear a hum or buzz when the system is off. In some cases, briefly turning the zone on will alleviate the matter temporarily. Doing so often results in a small audible "pop" as if it were relieving pressure at the output. In some areas, this action does not change anything.

I do not have info on the type of amp used. Sources and amps are all on the same power circuit. In my mind, this eliminates a ground loop scenario and points to a cheap noisy amp.

At present, every zone is an 8ohm stereo pair.

Is there something that can be done to bleed off this noise at the amp? Possibly a small resistor across the speaker outputs? Any suggestions?
 
In some rooms, I hear a hum or buzz when the system is off. In some cases, briefly turning the zone on will alleviate the matter temporarily
I suspect some speaker wires travel near Mains one, maybe even thrugh same or side by side conduit.

In that case induced/magnetically coupled Mains voltage will reach speakers, weak but audible in a silent room.
Turning amp ON places a virtual short across wires.

often results in a small audible "pop" as if it were relieving pressure at the output.
Simple turn-on Pop, don´t look any further

cheap noisy amp
Cheap amps are not noisy if OFF.
Is there something that can be done to bleed off this noise at the amp? Possibly a small resistor across the speaker outputs?
Nothing to "bleed" but you can kep amp ON.