Lipid rafts are thought to be key organizers of membrane-protein complexes in cells. Many proteins that interact with rafts have bulky polymeric components such as intrinsically disordered protein domains and polysaccharide chains. Therefore, understanding the interaction between membrane domains and membrane-bound polymers provides insights into the roles rafts play in cells. Multiple studies have demonstrated that high concentrations of membrane-bound polymeric domains create significant lateral steric pressure at membrane surfaces. Furthermore, our recent work has shown that lateral steric pressure at membrane surfaces opposes the assembly of membrane domains. Building on these findings, here we report that membrane-bound polymers are potent suppressors of membrane phase separation, which can destabilize lipid domains with substantially greater efficiency than globular domains such as membrane-bound proteins. Specifically, we created giant vesicles with a ternary lipid composition, which separated into coexisting liquid ordered and disordered phases. Lipids with saturated tails and poly(ethylene glycol) (PEG) chains conjugated to their head groups were included at increasing molar concentrations. When these lipids were sparse on the membrane surface they partitioned to the liquid ordered phase. However, as they became more concentrated, the fraction of GUVs that were phase-separated decreased dramatically, ultimately yielding a population of homogeneous membrane vesicles. Experiments and physical modeling using compositions of increasing PEG molecular weight and lipid miscibility phase transition temperature demonstrate that longer polymers are the most efficient suppressors of membrane phase separation when the energetic barrier to lipid mixing is low. In contrast, as the miscibility transition temperature increases, longer polymers are more readily driven out of domains by the increased steric pressure. Therefore, the concentration of shorter polymers required to suppress phase separation decreases relative to longer polymers. Collectively, our results demonstrate that crowded, membrane-bound polymers are highly efficient suppressors of phase separation and suggest that the ability of lipid domains to resist steric pressure depends on both their lipid composition and the size and concentration of the membrane-bound polymers they incorporate.