Precision surface engineering is key to advanced biomaterials. A new platform of PEGylated styrene–maleic acid copolymers for adsorptive surface biofunctionalization is reported. Balanced amphiphilicity renders the copolymers water-soluble but strongly affine for surfaces. Fine-tuning of their molecular architecture provides control over adsorptive anchorage onto specific materials—which is why they are referred to as “anchor polymers” (APs)—and over structural characteristics of the adsorbed layers. Conjugatable with an array of bioactives—including cytokine-complexing glycosaminoglycans, cell-adhesion-mediating peptides and antimicrobials—APs can be applied to customize materials for demanding biotechnologies in uniquely versatile, simple, and robust ways. Moreover, homo- and heterodisplacement of adsorbed APs provide unprecedented means of in situ alteration and renewal of the functionalized surfaces. The related options are exemplified with proof-of-concept experiments of controlled bacterial adhesion, human umbilical vein endothelial cell, and induced pluripotent cell growth on AP-functionalized surfaces.