I actually have quite a few books that are more or less Core D&D. I might have to flip through them to see just how high a level character one could make with no BAB.
The only annoying thing with such a crazy build is trying to figure out all the skills from so many different classes unless you house rule that once a skill becomes a class skill for the character, any class can add ranks to it as a class skill.
Even without dipping into PRC's I think i'll be able to get well over level 20.

I can see it now, guy wandering around with an animal companion, a familiar, and a psi-crystal...with all these various classes i might have to just make him true neutral.