Can your system be optimized to sound better for classical or non-classical?

Classical depends largely upon not compromising too much on tonality and instrument timbre whereas Rock and Pop thrive on punch and dynamics.

Of course, as usual, unavoidable loudspeaker compromises - as every loudspeaker designer wil only be too aware of - will depend upon which model you use. For example a JBL K2 will have different strengths and weaknesses compared to a Harbeth M40. Both excellent loudspeakers but neither of them are perfect.

It's precisely issues such as this that make system building and upgrading so difficult. Many times you can find yourself going forward in one area and back in another, even eventually arriving back at your starting point many years later. [Not that I know anything about this kind of foolishness of course - oh the pain!].

However as lowrider57 states above, it should still be possible to shuffle the various unavoidable compromises around so that your system can handle all genres reasonably well if you wish.

That's the unavoidable choice you always face when assembling a system - specialisation or generalisation.

As we know, despite our best efforts, no system gets anywhere near close to the real thing.

Go to the Salk Sound website and check out their SS7F speaker.

It has an "open back midrange" with 3 options: a) wide open
b) partially stuffed  c) closed off

These are options to help control room ambiance; and, it uses the example of listening to a live symphony versus a small jazz club.

Depending upon your equipment, the only item I could recommend would be a equalizer with user adjustable presets. You have the choice of a stand-alone unit or (if you're running your set-up with either a desktop or laptop) one of the on-line available programs.
Currently, I'm using a pair of Behringer 8024 eq's; one 'in-line', the other as a monitor with it's calibrated mic.
To update from these, I'd spring for their newest unit, the DEQ2496.  One of these could replace both, and add additional functions.   Just the 'auto room eq' to adjust your speakers to your listening space is an 'eye'...or should I say, 'ear opener'.  Pick up their calibration mic with it, and you're good to go. *S*
On line, there's a bevy of selections, but my 'go-to' is this:
https://sourceforge.net/projects/equalizerapo/
Add the Peace interface for the APO; it makes it more 'user friendly':
https://sourceforge.net/projects/peace-equalizer-apo-extension/?source=typ_redirect
If you listen to Anything online, this will 'do the deed' before the signal leaves your sound card. ;)  And has it's own memories; it also has more adjustment capabilities than you could likely ask for...

Oh, yeah...shop amazon for the 2496...don't pay full retail, and you get buyer protect as well. ;)

There's other 'fun stuff out there'...contact me direct if you've got any questions. *G*  Happy listening....

My system sounds great with everything because its high resolution.

I too spend a lot of time with classical (or, at least, serious music of any era). For me, the essence is clarity, tonality, and coherence from bass to treble.

Every component in the signal path has a sonic signature, and that most assuredly applies to EQ, regardless of technology or cost. I think that extra processing always gets in the way of serious music. For R&R of course, extra processing is the whole point.