  We explore the field induced magnetic phases of an $S=1$ $XXZ$ model with
single-ion anisotropy and large Ising-like anisotropy on a Shastry Sutherland
lattice over a wide range of Hamiltonian parameters and applied magnetic field.
The multitude of ground state phases are characterized in detail in terms of
their thermodynamic properties and the underlying classical (Ising limit) spin
arrangements for the plateau phases are identified by calculating the static
structure factors. The enlarged local Hilbert space of the $S=1$ spins results
in several new ground state phases that are not realized for $S=1/2$ spins.
These include the quantum paramagnetic state that is ubiquitous to $S=1$ spins
with single ion anisotropy, two different spin supersolid phases (with distinct
longitudinal ordering) and a magnetization plateau that arises as a direct
descendant of the 1/3 plateau due to quantum fluctuations that are not possible
for $S=1/2$ spins. We predict the same mechanism will lead to plateaus at
smaller fractions of 1/3 for higher spins. 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 as well as the
different longitudinal orderings.
