  We perform Monte Carlo simulations using the Wolff cluster algorithm of {\it
multiple} $q=2,3,4$ state Potts models on dynamical phi-cubed graphs of
spherical topology in order to investigate the $c>1$ region of two-dimensional
quantum gravity. Contrary to naive expectation we find no obvious signs of
pathological behaviour for $c>1$. We discuss the results in the light of
suggestions that have been made for a modified DDK ansatz for $c>1$.
