Extracting common waveform from two clips

Question

If one has an instrumental and non-instrumental version of a song, the vocals can be extracted by inverting the polarity of one of the sources, since the common audio cancels out.

However, what if my sources are two recordings of the same song with different unwanted audio on top of it? Imagine you recorded the same song from a video game twice, with different NPCs talking over it.

My logic was that I might be able to subtract one from the other, resulting in the offending sounds being isolated, then somehow subtract THAT result from the original clips to get only the part that is identical in both clips.

Is this possible, or is there some fundamental reason why this can't work? If it is possible, what are the steps involved?

Answer 1

I gave an answer to a similar question. The way that answer applies to your question is to regard the "song" as the "vocals" from the other question and the instances of "NPCs talking over it" as the "drums" and "saxophone".