Different amps for different music would be a real waste. One appropriate amp is all that should ever be required.
But it is probably useful to look at this a level higher. You can pretty easily accidentally put your system together which favors certain kinds of music. If you use say three CDs when auditioning equipment (or streamed tunes). Optimizing on those can send you in a direction to sub optimize others. It’s a system, so the speakers, amp, preamp, all effect the outcome. I loved the ethereal sound of some electronics CDs and had used them as test disks about 30 years ago and it had taken me off in a planar direction. Made several decisions that optimized these, but really sub optimized classical and rock. Which made me buy massive ss amps to power them. I started attending all acoustic classical music concerts regularly. I immediately, although completely unconsciously changed course and over ten years completely revamped my systems. Now all music types sound simply spectacular.
So you need compatible components that support each other… so you don’t have to swap out a component for particular music types. You could easily end up with two or three separate systems. But you also have to tune the whole system to the sound you value. I think the safest bet is true fidelity. I realized the importance for this when I started attending the symphony. I found that the symphony provides an actual empirical ruler to judge actual system fidelity. The symphony provides sound levels from the very quietest to the maximum volume, every variety of instrument, in solo and en mass, un-amplified, unmastered. Live acoustic jazz also helps. But amplified electronic, rock, etc. are subject to amplification live so are not good for a reference. With this as a reference you have a target… and all music types will rise in quality as your system improves. You will still have cuts to audition, but if behind it all you have a real absolute ruler, you have a guiding light.
Just some thoughts about how to aim at system design.
