I believe some of the caps in question typically go between the battery and the amplifier in a car setup. This is probably more to compensate the alternator/battery capacity than the amplifier itself. However, as this article points out (
https://axleaddict.com/cars/Car-Audio-CAPACITORS-Why-They-DONT-Work), it may not work quite as you think it will since the source of the current is supposedly limited as it is and will need to recharge the capacitor when it drains (i.e. it's going to the cap instead of your amp at that point) so unless the audio event in question is pretty small/momentary with much less demand afterwards (certainly possible for bass kicks I suppose), you might do more harm than good. I'm guessing it helps some situations and harms others. It would be very content dependent. Since it's mostly used with subwoofers in mind, small kicks could benefit. Longer ones could starve your main speaker amps. You're probably better off with a larger alternator.
Inside the amplifier there are filtering caps and there are storage caps in any given design. You can take those out and upgrade them to better quality and/or higher capacity. The designers probably choose the caps based on the projected cost of the overall amplifier design. High end amps get better caps for both filtering and storage. Large capacity caps (or banks of smaller ones as they can respond faster than large electrolytic ones) aren't cheap and thus it seems like it should certainly be possible to upgrade them in lesser designs. You would need to know what you're doing, of course. Is it worth the bother? I dunno. Some people live for that sort of tinkering. I'd prefer to get an amplifier with a larger continuous capacity, personally.
This thread has some interesting conversation and info on the subject:
https://www.hometheaterforum.com/community/threads/capacitors-in-amps-can-they-be-upgraded.56721/
I noticed Cary Audio will upgrade your caps for you on a Cary brand amp (for a price), although they seem to be more about supposed "quality" than increasing headroom:
https://www.caryaudio.com/upgrades-and-modifications/