  We study the nature of the ground state of the strongly-coupled two
dimensional extended boson Hubbard model on a square lattice. We demonstrate
that strong but finite on-site interaction U along with a comparable
nearest-neighbor repulsion V result in a thermodynamically stable supersolid
ground state just above half-filling, and that the checker-board crystal is
unstable for smaller V, and for any V just below half-filling. The interplay
between these two interaction energies results in a rich phase diagram which is
studied in detail using quantum Monte Carlo methods.
