In receptor-mediated endocytosis, cells exercise biochemical control over the mechanics of adhesion to engulf foreign particles, featuring a variable adhesion strength. Here we present a thermodynamic model with which we elucidate that the variable adhesion strength critically governs the cellular uptake, yielding an uptake phase diagram in the space of ligand density and particle size. We identify from the diagram an endocytosed phase with markedly high uptake, encompassed by a lower and an upper phase boundary that are set, respectively, by the enthalpic and entropic limits of the adhesion strength. The phase diagram may provide useful guidance to the rational design of nanoparticle-based therapeutic and diagnostic agents.