In my experience (which is very, very short if any) i've seen that when your lights dim while your volume is loud, is not always because of a weak alternator, but a slow current regulator.
I got confused that I could see a very, very minimal change in my lights when I put my stock radio (KENWOOD KDC-217, with my two stock frontal speakers) at a little high volume. Similar as when you have your intermitent lights on
I guess, there's nothing to do, only adding a capacitor (IN THIS SPECIFIC CASE) to help that.