  Twisted bilayer MoTe$_2$ is a promising platform to investigate the interplay
between band topology and many-body interaction. We present a theoretical study
of its interaction-driven quantum phase diagrams based on a three-orbital
model, which can be viewed as a generalization of the Kane-Mele-Hubbard model
with one additional orbital and long-range Coulomb repulsion. We predict a
cascade of phase transitions tuned by the twist angle $\theta$. At the hole
filling factor $\nu=1$ (one hole per moir\'e unit cell), the ground state can
be in the multiferroic phase with coexisting spontaneous layer polarization and
magnetism, the quantum anomalous Hall phase, and finally the topologically
trivial magnetic phases, as $\theta$ increases from $1.5^{\circ}$ to
$5^{\circ}$. At $\nu=2$, the ground state can have a second-order phase
transition between an antiferromagnetic phase and the quantum spin Hall phase
as $\theta$ passes through a critical value. The dependence of the phase
boundaries on model parameters such as the gate-to-sample distance, the
dielectric constant, and the moir\'e potential amplitude is examined. The
predicted phase diagrams can guide the search for topological phases in twisted
transition metal dichalcogenide homobilayers.
