  We study the physics of cold polar molecules loaded into an optical lattice
in the regime of strong three-body interactions, as put forward recently by
B\"uchler [Nature Phys. 3, 726 (2007)]. To this end quantum Monte Carlo
simulations, exact diagonalization and a semiclassical approach are used to
explore hardcore bosons on the two-dimensional square lattice which interact
solely by long ranged three-body terms. The resulting phase diagram shows a
sequence of solid and supersolid phases. Our findings are directly relevant for
future experimental implementations and open a new route towards the discovery
of a lattice supersolid phase in experiment.
