Hi Tony.

It would probably amplify the classical part at the expense of some clipping, or attenuate the Pop part to a very low volume. At least if the "loud" part of the classical one was long enough. AFAIK, that type of software still avoids clipping if possible.
And no, like I said, I know how that type of software should work, and that there are some such programs out there, but don't know any specific package that uses this approach. I have a tendency to absorb interesting facts about different technical things but to forget about real world implementations of that. Sorry. If I stumble about some such software, I will say so in here.

cu,
sven