I don’t think an amp could be able to change the frequency response of headphones, but some people say it can, but why could it? How can an amp change the sound? Only talking about solid state because I don’t know much about tube amps. An amp increases the amplitude of the signal, this would evenly increase the signal throughout the frequency range, I don’t think there is a way to boost the low frequency signal more than everything else. It’s all analog so there is no DSP, it receives an analog signal and outputs an analog signal. If there is something inside it that can change the sound from an analog signal, then a cable could also change the sound using the same technique.
I know some multi driver IEM can use an impedance adapter to change sound by changing the ratio of how much power one driver gets over the other, making it relatively louder than the other. But this won’t work for headphones.
Just to add to this. Amplifiers aren’t unique to headphones. While headphone amplifiers shouldnt change the FR that doesn’t mean they can’t. Just look at guitar amplifiers and you will see tone stacks where you cut treble, mids or bass. From an EE standpoint they are the same
Search for “frequency response”. An ideal amp would amplify all frequencies evenly, but there’s no such thing. Also have a look at your great grandma’s tube radio, it has knobs for bass and treble, and it surely has no DSP.
Use google, I’m sure engineers and audiophiles have explained it a thousand times in detail. Amps are physical devices utilizing all sorts of parts and op-amps etc, the signal interacts with all of these parts as it passes through, those parts are not identical in any given device so the ‘interaction’ won’t be either, it’s physics. Also, there are people who believe the cable makes a difference, I can’t say I do, but plenty do.