  We study the ground-state properties of ultracold bosons in an optical
lattice in the regime of strong interactions. The system is described by a
non-standard Bose-Hubbard model with both occupation-dependent tunneling and
on-site interaction. We find that for sufficiently strong coupling the system
features a phase-transition from a Mott insulator with one particle per site to
a superfluid of spatially extended particle pairs living on top of the Mott
background -- instead of the usual transition to a superfluid of single
particles/holes. Increasing the interaction further, a superfluid of particle
pairs localized on a single site (rather than being extended) on top of the
Mott background appears. This happens at the same interaction strength where
the Mott-insulator phase with 2 particles per site is destroyed completely by
particle-hole fluctuations for arbitrarily small tunneling. In another regime,
characterized by weak interaction, but high occupation numbers, we observe a
dynamical instability in the superfluid excitation spectrum. The new ground
state is a superfluid, forming a 2D slab, localized along one spatial direction
that is spontaneously chosen.
