  We use large scale quantum Monte Carlo simulations to study an extended
version of the canonical Shastry-Sutherland model -- including additional
interactions and exchange anisotropy -- over a wide range of interaction
parameters and an applied magnetic field. The model is appropriate for
describing the low energy properties of some members of the rare earth
tetraborides. Working in the limit of large Ising-like exchange anisotropy, we
demonstrate the stabilization of columnar antiferromagnetic order in the ground
state at zero field and an extended magnetization plateau at 1/2 the saturation
magnetization in the presence of an applied longitudinal magnetic field --
qualitatively similar to experimentally observed low-temperature phases in
ErB$_4$. Our results show that for an optimal range of exchange parameters, a
spin supersolid ground state is realized over a finite range of applied field
between the columnar antiferromagnetic phase and the magnetization plateau. The
full momentum dependence of the longitudinal and transverse components of the
static structure factor is calculated in the spin supersolid phase to
demonstrate the simultaneous existence of diagonal and off-diagonal long-range
order. Our results will provide crucial guidance in designing further
experiments to search for the interesting spin supersolid phase in ErB$_4$.
