  Two-dimensional magnetic insulators can be promising hosts for topological
magnons. In this study, we show that ABC-stacked honeycomb lattice multilayers
with alternating Dzyaloshinskii-Moriya interaction (DMI) reveal a rich
topological magnon phase diagram. Based on our bandstructure and Berry
curvature calculations, we demonstrate jumps in the thermal Hall behavior that
corroborate with topological phase transitions triggered by adjusting the DMI
and interlayer coupling. We connect the phase diagram of generic multilayers to
a bilayer and a trilayer system. We find an even-odd effect amongst the
multilayers where the even layers show no jump in thermal Hall conductivity,
but the odd layers do. We also observe the presence of topological proximity
effect in our trilayer. Our results offer new schemes to manipulate Chern
numbers and their measurable effects in topological magnonic systems.
