It would be hard to accurately diagnose your problem without many more details about your system. But here is just a guess as to a potential cause(s) based on the little information supplied.
The larger power demand of the collective amplifiers is modulating the voltage supply to the HU. In other words, as the amplifiers draw substantial current the voltage supply to the HU sags. So to remedy this, at least in part, run a direct supply for the HU ground, switched B+, and constant B+ directly to the identical battery source that is supplying the amplifiers. Use no less than 14-gauge wire. Focus on quality terminations and connections. Completely bypass the protracted path of the factory wiring harness.
Now the amplifiers must each have adequate supply cable and the battery must have adequate supply from the engine block ground and alternator. And the batteries must be in good condition and in a good state of charge. The only way to really be certain is to measure the voltage at rest and under load. If the batteries are run down below 12.0 volts then it won't be long before those batteries are failing you.
Hopefully the HU is presently grounded via a better source than through the floating RCA grounds but following the above instructions would remedy that also.
Be careful about what you are using as a remote turn-on for the amplifiers. I would use the HU output trigger to operate a relay which in turn supplies the amplifiers with a trigger.
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