Nonlocal effects in metal–dielectric (MD) periodic nanostructures may typically be observed when the plasmonic particles and gaps are on the scale of a few tens of nanometers, enabling under certain conditions (succinctly for epsilon near zero) a collimated beam to split into three refracted signals. We developed a method for precisely evaluating the categorized transmissivity in an air/trirefringent metamaterial interface, which uses a fast one-dimensional Fourier transform and finite element solvers of Maxwell’s equations. In periodic arrays of MD nanofilms, it is proved a tunable transmissivity switch of the multirefracted beams under varying angle of incidence and wavelength, while keeping reduced levels of reflectivity. Low-loss trirefringent nanomaterials may enable the development of ultracompact and tunable light splitters and modulators.