  We investigate a simplified continuum model of a twisted homotrilayer TMD
with negligible next-nearest layer couplings. We systematically analyze band
structure and topology of various stacking configurations in a twist angle
range from $1^\circ$ to $4^\circ$. This allows us to uncover a plethora of
topological transitions as well as various angle regimes with flat bands - some
of them topologically non-trivial, which are of growing interest for the
realization of exotic strongly correlated phases. Additionally, we uncover
surprising properties, such as that for certain stacking configurations, some
layers effectively decouple from other layers. In this case, the only remnant
of coupling between layers is a layer-dependent energy shift.
