In commercial installations, we used to do a thing we called 'bridging' with a 10kOhm resistor to each amp input. Since all the amps were generally in the same rack and running off the same AC source, we did not worry about ground loops. In any event, with unbalanced signal connections, the signal 'ground' is also the return path for the signal, so you cannot very well do without it.
For four amps, that meant 4 10kOhm resistors, of course; Wattage is not critical, since you would not expect there to be more than a tiny amount of current flow. This keeps at least 20kOhm between any two amp inputs, which we normally found to be enough to keep any interaction between the inputs to a minimum.