  We study systems of M Potts models coupled by their local energy density.
Each model is taken to have a distinct number of states, and the permutational
symmetry S_M present in the case of identical coupled models is thus broken
initially. The duality transformations within the space of 2^M-1 multi-energy
couplings are shown to have a particularly simple form. The selfdual manifold
has dimension D_M = 2^{M-1}-1. Specialising to the case M=3, we identify a
unique non-trivial critical point in the three-dimensional selfdual space. We
compare its critical exponents as computed from the perturbative
renormalisation group with numerical transfer matrix results. Our main
objective is to provide evidence that at the critical point of three different
coupled models the symmetry S_3 is restored.
