In this work, we present an atomistic-resolution MD simulation study of the accretion of lipid monomers towards mixed micellar assemblies. We simulated binary mixtures of five lipid types in different ratios, observed their aggregation, and measured the influence of the micellar composition on the kinetics of monomer entry and exit. We report that compositional changes do indeed affect these rates, and to various extents for different lipid types, lending credence to the realism of network-like mutually-catalytic interactions among lipids. We describe cohesive aggregation profiles for discrete lipid combinations, and calculated the accretion flux of our mixed micelles, and determined that some may attain compositional homeostasis in non-random configurations, supporting predictions by the GARD model.