We show that the scattering rate for any non-relativistic perturbative four fermion interaction between dark matter (DM) and electrons in any target is proportional to several measurable material properties, encapsulated by a single master formula. This generalizes the dielectric function formalism—originally developed for DM interactions that couple to electron a much broader class of interactions, incorporating both spin-dependent and spin-independent interactions simultaneously. This formalism links the full many-body response of a target system to the DM probe in a clear and simple form, providing a reliable event rate prediction from measurable material quantities. We demonstrate the utility of our formalism by placing new limits from existing data on a class of spin-dependent light DM interactions, as their rates are determined entirely by the dielectric function. We further highlight a promising avenue for the detection of sub-MeV DM using the rare-earth metal Praseodymium, which exhibits a spin-dependent anisotropic response down to the meV scale. Our results lay the groundwork for a rapid systematic investigation of novel electron scattering targets going beyond the classic spin-independent searches, enhancing the prospects for DM detection.