Good, you're talking about the mid range, not the low or high frequencies. My first guess is that it could be the off-axis performance of your speakers can be best heard only at high volumes. Try this:
- Find a quieter musical passage, ideally with a single voice or instrument. A female voice or brass horn (trumpet or french horn) is a good choice because it often has first harmonic overtones at about the same frequencies as the crossover between mid woofer and tweeter.
- Listen with only one speaker not both. Listen at low volume and at high volume.
- Walk around the room, listening directly in front of the speaker and off to the sides. Does the sound of the voice or instrument loose any sound quality as you move off to the sides?
If so, the off-axis performance of your speakers is much weaker than the on-axis performance. Your speakers tend to beam, rather than spread those sounds around the room. At high volumes you may be able to hear enough off-axis sound for things to sound good. But at low volumes you mainly hear only the on-axis sound. It can be hard to pin down, but it sounds like something is missing. From what you said, I think this may be going on.
As you probably normally listen in stereo and while sitting in the sweet spot, what you hear is a combination of the direct on-axis sound and the off-axis sound, much of which can be reflected off walls. This combination is what makes for a more realistic and pleasant sound. The balance in a speaker's on-axis and off-axis performance is what makes for that "out of the box" sound where musicians seem to be sitting in your room, rather than inside your speakers.
There too many snarky comments here for my tastes too.
Amps and their distortion levels seem to have little to do with your question. In my experience, I don't hear amp distortion levels until they are higher than 1%. And I don't remember any amp I've heard in decades with performance that poor. Speakers can distort at levels 10 times higher that, especially in the bass frequencies.