For quite a while in the first half of the 20th century, many physicists tried to concoct some manner of unified theory to explain all known phenomenon, a lot of them using geometric theories (ie teleparallelism, affine gravity, asymmetric metric theories, Kaluza-Klein, etc). While their main goal was the unification of general relativity and electromagnetism, there was also the hope that it would explain quantum phenomenon, by outputting some discrete sets of solutions.
As far as I know, none of them succeeded in that domain. What I want to know is, was there ever any hope of it? Can a classical theory, be it a field theory, of extended objects or geometric, have a discrete spectrum, or does it by its very structure (perhaps via some theorems on differential equations or whatever else) force it to have a continuous spectrum for all variables? Also just in case, did any such theory ever succeed at least in that aspect, even if it failed in other aspects to describe quantum mechanics?