  We address the intensively studied extended bosonic Hubbard model (EBHM) with
truncation of the on-site Hilbert space to the three lowest occupation states
n=0,1,2 in frames of the S=1 pseudospin formalism. Similar model was recently
proposed to describe the charge degree of freedom in a model high-Tc cuprate
with the on-site Hilbert space reduced to the three effective valence centers,
nominally Cu^{1+;2+;3+} . With small corrections the model becomes equivalent
to a strongly anisotropic S=1 quantum magnet in an external magnetic field. We
have applied a generalized mean-field approach and quantum Monte-Carlo
technique for the model 2D S=1 system with a two-particle transport to find the
ground state phase with its evolution under deviation from half-filling.
