Tonal changes linked to volume control settings; can it really be so?

Hello. In summary, should the tonal characteristics of an amp be consistent across at least 80 percent of its volume control range?

Let me explain if I may. I've heard tell of a person – and he might not be the only one – who while using a sophisticated integrated amp (the brand is irrelevant in this context I think and might be a distraction from the core issue) notices a change of tone that is linked to the volume. Thus, apparently, he is struggling to achieve concurrently the volume he likes plus the tone he likes. He can achieve one, or the other – but not both. This is particularly apparent on well-recorded solo instruments and female voice.

A lack of bass at low volumes isn’t the issue here though. It’s tonal characteristics in the low mid to top spectrum.

Room acoustics must of course play a part but it seems not to be the most significant contributor. I don't have the details re this and so can't elaborate.

Frankly I've not experienced this in the audio world but … I am well aware of it with my bass guitar rig inasmuch as with the gain and vol controls on my SWR BabyBlue combo amp, I get the precise tone I want (Epiphone Jack Casady) at one particular setting on the guitar volume bass control. This is with me leaving the guitar bass controls untouched. Apparently most musicians experience this; it’s commonplace.

Perplexed, I spoke to a well known designer of studio systems. This volume versus tone issue is, again, frequently encountered in that world.

While I've yet to confront this on my modern home system I think (and I use the word advisedly here) I hear it via some of my vintage amplification.

Has anyone here experienced something similar? Thanks. Howard.