I’ve seen people state both that they so not influence the tuning as long as they deliver the same power and others stating that they can make headphones “sound warmer” or “brighter”. I don’t see how that would happen though and a lot of audiophiles just hear things that I feel aren’t there, like some noise difference between the Apple DAC Dongle and a 500 EUR DAC using an off the rack chip.
Take this comment from ASR:
Amps are more likely to make an audible difference than most DACs, but that certainly doesn’t mean there are audible differences between most amps
I’m talking purely about AMPs here, not a DAC combination.
They can, but it really depends in what you are driving. Most solid state amps today aim for a true flat response and are capable of achieving it when driving most headphones and, probably, all IEMs. You usually will not notice an amp deviating from that flat response unless you are making it work hard. Whether that be via power or gain. Additionally, you probably wont notice the deviation as much on a solid state amp as you would on a tube amp.