Engineering synthetic cells with biomimetic surface architectures requires precise control over the spatial organization and mechanical properties of the membrane surface. Inspired by the protective and regulatory functions of the natural glycocalyx, we present a modular platform for constructing hierarchical, crosslinked PEG networks on fluid lipid membranes. Through spatially controlled, sequential strain-promoted azide-alkyne cycloaddition (SPAAC), we assemble a tunable, multilayered PEG mesh that mimics the dynamic, dense, and mechanically resilient architecture of the glycocalyx. By incorporating linear PEG lipids as defined anchors at controlled densities (0.25-1 mol%), we establish a reactive scaffold on the membrane surface. Sequential conjugation with eight-arm PEG-DBCO and eight-arm PEG-azide enables the formation of a covalently crosslinked, multilayered PEG mesh with tunable thickness, connectivity, and mechanical robustness. The multivalency of the eight-arm architecture allows each first-layer PEG to act as a branching node, enabling high-density network formation and exceeding the surface coverage achievable with linear PEG chains. Crucially, the phase-dependent partitioning of the lipid anchor enables a spatially confined network assembly within the liquid-disordered (L) domains of phase-separated membranes, allowing for domain-specific functionalization. Once formed, the crosslinked network exhibits persistent spatial organization, retaining its footprint even after thermal mixing of the underlying lipid phase-a hallmark of mechanical stability and functional memory. Quantitative analysis QCM-D and FRAP reveals that network connectivity and lateral mobility are governed by anchor density and PEG architecture. The resulting mesh acts as a tunable steric barrier, effectively attenuating receptor-ligand interactions in a stepwise, assembly-dependent manner. This work demonstrates a powerful strategy for engineering programmable, adaptive, and mechanically resilient surface architectures on model membranes, a critical step toward interfacing functional synthetic cells with intelligent nanocarriers of spatiotemporally regulated functionality.