  Moir\'e lattices formed from semiconductor bilayers host tightly localised
excitons that can simultaneously couple strongly to light and possess large
electric dipole moments. This facilitates the realization of new forms of
polaritons that are very strongly interacting and that have been predicted to
lead to strong optical nonlinearities controlled by multi-photon resonances.
Here, we investigate the role of the non-local component of the exciton-exciton
(dipolar) interactions on the optical response of these strongly-interacting
moir\'e exciton-polaritons under conditions of strong optical driving. We find
that the non-local interactions can strongly influence the steady-state
properties leading to multi-stabilities with broken translational symmetry and
pronounced distortions of the multi-photon resonances. We develop a
self-consistent approach to describe the steady-state solution of moir\'e
excitons coupled to a cavity field, treating the long-range interaction between
the excitons and the photon field at the semi-classical level.
