Hi Jay,
Short of cutting up your track into individual notes, all you can really do is boost or cut the approximate range for a given harmonic. From my inspection of your bass track spectrum I guess the fundamental frequency range for the played piece is probably from around 80Hz to 220Hz with most notes falling in range from 100-200Hz. So, for example, if you want to suppress sencond harmonic output then you should be applying a cut in the frequency range from 200-400Hz. That really is about the limit to what you can do with simple filtering.
To actually do a good job at altering the harmonic content of a single instrument you would need to use a different approach in a very specific application - maybe a filterbank or pitch tracking and a tracking notch filter. It should be relatively straight forward to implement something along those lines for a track of only one instrument, but multiple instruments would make it almost impossible to do well. Sounds like a good idea for a very specific product. I don't have the time to look at it though.
Paavo.