  Understanding quantum many-body systems is at the heart of condensed matter
physics. The ability to control the underlying lattice geometry of a system,
and thus its many-body interactions, would enable the realization of and
transition between emergent quantum ground states. Here, we report in-situ gate
switching between honeycomb and triangular lattice geometries of an electron
many-body Hamiltonian in R-stacked MoTe2 moir\'e bilayers, resulting in
switchable magnetic exchange interactions. At zero electric field, we observe a
correlated ferromagnetic insulator near one hole per moir\'e unit cell
({\nu}=-1), i.e., a quarter-filled honeycomb lattice, with a widely tunable
Curie temperature up to 14K. Fully polarizing layer pseudospin via electric
field switches the system into a half-filled triangular lattice with
antiferromagnetic interactions. Further doping this layer-polarized
superlattice introduces carriers into the empty layer, tuning the
antiferromagnetic exchange interaction back to ferromagnetic. Our work
demonstrates R-stacked MoTe2 moir\'es to be a new laboratory for engineering
correlated states with nontrivial topology.
