There are plenty of distortions that have sonic consequences but are below the current ability to measure. So you can have amp A with 0.1% THD being more transparent than amp B with 0.01% THD as other distortions are subjectively more important. For example, you will never measure problems with interconnect cables, but you can hear the effect of changing interconnect cables. So I am not saying that just because something measures better than something else does not mean it will sound better. But, if you reduce measurable distortion, with every other effect not changing, you will get an improvement in SQ. Measurements are very important, as they tell you what is wrong objectively.
Now if you need more power, then add another amp, no argument from me here; but by adding an extra amp when you do not need more power, then you will degrade transparency - you are using colourations to suit your taste. Now if you prefer to add some softness to the sound, by adding some 2nd harmonic distortion say, then that's fine, whatever suits you - but it's not what I try to do. my journey over the last 35 years is to try to understand all distortions (not just THD but all changes to the original), and to engineer a solution to these distortions to make them as small as possible, so that the device is as transparent as possible. Why do I do that? Because I believe that is the way to make something musical, and musicality - that is enjoying music - is what I think it is all about.
So why would transparency make it more musical? Principally two reasons - variation, and brain strain. Now variation - the ability to hear contrasting dynamic, rhythm, timbre, sound stage and separate instruments is crucial to musicality. Going back to the addition of softness by adding 2nd harmonic would mean that everything always sounds soft, so you lose out in variations, which then impacts musicality. Now brain strain (I don't mean listening fatigue here) is about how easy the brain separates sound out into the illusion of instruments occupying a tangible space. Now the brain does an incredible job of separating sounds out into discrete entities, and does this using some kind of processing; how, science does not understand. But adding audible distortion will affect the brains ability to process the sound, so it becomes harder for the brain to make sense of the sound. Now if the brain is straining, then the brain is working on trying to make sense of the sound, rather than enjoying the music; plus you get long term listening fatigue as the brain is constantly working on trying to separate individual sounds out that have been corrupted by distortion.
So what does one do if a HP is too bright? My advice is not to add distortion via an extra amp, but to either replace the HP, or use some gentle EQ, or try other cables (that's a minefield). But at the end of the day, whatever makes you enjoy music more is what is important.
Rob