Killing the last bit of unwanted noise

Hi, recently purchased a used integrated amp (gryphon callisto) which I love. When no music is playing the amp is dead quiet with no hiss etc. at the speakers, even with the volume turned up. However, if I listen to music (loudish) I detect some “noise”, especially around the higher frequencies that just rob the sound from the last bit of transparency and adds what I can best describe as a veil in the upper registers. Now, this is still far better than most amps I have heard and think this is pronounced a bit as the sound is so transparent…. But hope I can get this just a tad better with some mods.

Is there anything I can do to reduce this (cabling, power conditioner etc.) or is this just part of the package I have to settle for? As the amp runs quiet when no music is playing I assume the noise is introduced somewhere else in the chain