A very good question.
I have some pieces of answers (partly subjective) - I will add them here tonight after a family trip.
*Updated:.
First, there is a difference between electronic/digital recordings and acoustic ones with live instruments.
For the former there are no frequency limits - deep sub-bass (below 30-50 Hz) and the last octave (10 to 20 kHz) can be plentiful and well-defined. For those, a neutral signature, like that of Crin's tuning oreferences (exemplified to me by Dioko or reasonably by Hola) will do best as transducers.
By contrast, acoustic tecordings of subbass require large oscilating structure and proper mics to capture it, as well for the last octave, not so much overtones are there, while sibilance present a lot of problems for mics to record cleanly.
Now, many good classical recordings present a more extreme case of acoustic recording made for older acoustic reproduction and vinyl, as nicely pointed out by
@Nimweth here.
In the Science forum, I was once given a test file of the "epitome" of the golden recordings - revelationaly, nothing above 10 kHz, and very strongly tapered above 3-4 kHz. This was done to cut vinyl noise and to concentrate on mids, where the 'core information" is.
Correspondingly, transducers that enhance treble, largely so from 1 to 4 kHz (where there is something to enhance) work well; reproduction past 10 kHz is really needed. Translates to a seemingly crazy pina gains of above 12-15 dB *but works, IMHO).
(Now, there are definitely modern audiophile classical recordings that already enhance treble and use closer mics fir more overtones - so they will work better with different IEMs, I did not encounter too many of prominent cases though).
Then multiple transducers work well to separate abd reproduce more overtones, as pointed out below.
So all-BA work well. To me KZ AS16 is the epitome of an IEM for classical music.
BA10, a newer version of AS12 and AS16 pro are also great.
AS16 pro may be the one to try, if you did not experience it. If liked and leaner and more treble enhanced - AS16 original. If more eefinement is needed - more expensive all-BA may be the way to go (where I have little experience), I do like some roughness and granularity in IEMs - works well for me for violin recordings.