It would be wonderful to be able to go back to a previously profiled amp and do the refine over again and try to make it better. I realize without the original setup you wouldn't be able to compare the real amp to the profiled amp, but my observation is that the more different sounds you use in the refine step the more accurate it becomes. And if you refine some more it again becomes more accurate.
When I profile, for the refine step I use a prerecorded guitar sequence of chords, slaps, highly dissonant chords and all of the sound I can from the guitar. The track also has these sounds from several guitars. It works extremely well, but still not 100% exact. I think I could make a better track with more sounds, so the re-refine would be nice.
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