Low-energy compute-in-memory architectures promise to reduce the energy demand for computation and data storage. Wurtzite-type ferroelectrics are promising options for both performance and integration with existing semiconductor processes. The Al_1-xSc_xN alloy is among the few tetrahedral materials that exhibit polarization switching, but the electric field required to switch the polarization is too high (few MV/cm). Going beyond binary compounds, we explore the search space of multinary wurtzite-type compounds. Through this large-scale search, we identify four promising ternary nitrides and oxides, including Mg₂PN₃, MgSiN₂, Li₂SiO₃, and Li₂GeO₃, for future experimental realization and engineering. In $>$$>$90% of the considered multinary materials, we identify unique switching pathways and non-polar structures that are distinct from the commonly assumed switching mechanism in AlN-based materials. Our results disprove the existing design principle based on the reduction of the wurtzite c/a lattice parameter ratio when comparing different chemistries while supporting two emerging design principles—ionicity and bond strength.