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 moiré bilayers, resulting in switchable magnetic exchange interactions. At zero electric field, we observe a correlated ferromagnetic insulator near one hole per moiré unit cell (v=-1), i.e., a quarter-filled honeycomb lattice, with a widely tunable Curie temperature up to 14K. A 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 moirés to be a new laboratory for engineering correlated states with nontrivial topology.