Several contributing factors here. Volume control non-linearities occur frequently, but seldom account for the severity of the problem you describe. But, it IS a matter of non-linearity, but more generalized throughout your entire system(s). Although some amps may have a bit more difficulty playing at, say, low listening levels, especially when paired with some speakers, I'll assume this is not really the main cause here. I'll also assume that your speakers and amps have been well enough matched to each other impedance-wise and power-wise...that your wiring is of the appropriate gauge and the your amp's watt rating is either right around or slightly above your speakers rating.
If all that checks out, then I would say that you are actually dealing with a power treatment issue. Too much audible hash from electrical noise (everybody has it, whether they're aware of it or not) will cause exactly your result.
You can try the cheap stuff from Furman, IsoTek, Panamax, Monster and the like, or you can try the more expensive stuff that will not introduce negative impacts on the sound, like Bybee Devices or Alan Maher Designs. But, any of those should have some impact and the closer you get to an effective solution for it, the bigger the sweet spot will become. It is possible to take things as far as winding up with a Completely linear system (an impressive animal, to be sure), but it may entail considerable expense to actually get all the way there.
Hope that helps.