One program that sort of does that (but is actually impossibly cooler) is Melodyne, by Celemony. It doesn't work with mp3's, but it can read polyphonic .wav files (although, I'm not sure if it yet has the capability to read a full mixdown). You can edit each note of a chord individually in a midi-like manner, micro-tune, change formant and everything. It's actually the coolest thing ever.
It's not exactly free, though (EUR 299.00 for the VST or EUR 699.00 for the standalone)