Just an FYI, but our hearing's "frequency response" changes depending on level. At lower levels, we are less sensitive to the lowest and highest frequencies, and midrange becomes more dominant. As you go up in level, the response begins to get more even. You can see this in the classic Fletcher-Munson equal loudness curves and is why stereos back in the day commonly had a "loudness" switch which gave a bit of boost to the lows and the highs so that things would sound a bit more natural when listening at lower volumes.
I agree with you Steve that this is the normal behavior on most headphone and speakers system.
On some speakers, like the Apogee Diva, I found that is the midrange that loosens up the most on higher volume. IMHO Diva and other headphones/speaker system that has a very full midrange, have like a bit of lack of clarity in the mids (relatively speaking) then played on lower volume, but then power up they rely sing. Other component, then the headphones and speakers, in the system will also inflect on this.
On Linn Klimax 350, with is a fast and good speaker, but IMO don’t have a very full/warm midrange that’s not the case. For me the LCD 3 behave like the Diva and the He-500 like the Klimax.
From my experiences most system will benefit in some ways from a little higher volume, but the ones with a very full midrange will advantage even more because of improved clarity for voices, piano and so on.