  We study a gas of repulsively interacting bosons in an optical lattice and
explore the physics beyond the lowest band Hubbard model. Utilizing a
generalized Gutzwiller ansatz, we find how the lowest band physics is modified
by the inclusion of the first excited bands. In contrast to the prediction of
the lowest band Bose-Hubbard model, a reentrant behavior of superfluidity is
envisaged as well as decreasing width of the Mott lobes at strong coupling.
