Hi Again, Sig.
Maybe I'm not up to speed on my terminology--
when you say "overdrive," does that means that you are looking for an fx processor that adds various kinds of distortion to your signal? Like a guitar overdrive? If so, you may want to check out some of the rack-mount processors made for guitarists. Several of the major guitar amp manufacturers make them. Even though it's marketed toward guitarists, a signal is a signal-- I don't suppose the unit would mind processing a human voice or pan flute for that matter.
Cheers!