If for instance you have a sound or voice, and it start's at pitch middle C, then you shift it down by say, 8 semitones, what appears to happen often is that the higher frequencies become shifted so that there's no longer any high frequencies to the voice whatsoever. What can be done to counteract this?
If you have to pitch shift plus/minus by more than ~4 semitones (M3), then you are probably better off just re-recording the vocal track in the different key. You'll never be able to reproduce the harmonic spectrum of the vocalist correctly after pitch shifting by large amounts. To do that you would need a model of the performers vocal track including how its resonances/formants vary with frequency and amplitude. Besides a harmonic exciter, you could also try using a match EQ where the spectrum to match is the original un-pitch-shifted vocal track. So keep a copy of the original untranspose track, and use that as the spectrum to match while processing the transposed track. Then after the match EQ, maybe try the harmonic exciter. I'm not sure what order would work best, but theoretically it would seem to make sense to do the match EQ first, and then the harmonic exciter if needed.
You could use a harmonic exciter plug-in, to add the sparkle back to the higher frequencies.
These are quite often used for vocals, so is probably the best choice for the task.