  We show how to couple two critical Q-state Potts models to yield a new
self-dual critical point. We also present strong evidence of a dense critical
phase near this critical point when the Potts models are defined in their
completely packed loop representations. In the continuum limit, the new
critical point is described by an SU(2) coset conformal field theory, while in
this limit of the the critical phase, the two loop models decouple. Using a
combination of exact results and numerics, we also obtain the phase diagram in
the presence of vacancies. We generalize these results to coupling two Potts
models at different Q.
