The addition of trace molecules into membranes can significantly alter the morphology of the co-existing liquid phases and lipid phase transition temperature. Membrane additives may affect lipid phase dynamics through preferentially partitioning to the boundary between lipid phases or preferentially mixing into one lipid phase. The characteristic differences between these mechanisms are demonstrated here in a minimalistic nearest neighbor model to provide a framework for how slight changes to membrane composition may affect lipid-phase-dependent processes, such as lipid-raft formation, immunological signaling, and molecular sorting preceding endocytosis with coexisting liquid phases. Within the low mole fractions explored here (≤3 mol%), increasing the additive concentration linearly changed the phase miscibility temperature. Rotationally asymmetric Janus particles reduced the miscibility transition temperature for all fractions and degree of phase polarization. Rotationally symmetric additives, however, either increased or decreased the phase miscibility temperature depending on the phase preference of the additive. While most experimental molecules may contain aspects of both of these idealized additives, this model provides a broad framework to quantify the effects of membrane additives in regard to lipid phase preference, lipid-raft association, and contribution to lipid phase-dependent molecular sorting.