High colloidal stability in aqueous conditions is a prerequisite for fluorescent nanocrystals, otherwise known as "quantum dots", intended to be used in any long-term bioimaging experiment. This essential property implies a strong affinity between the nanoparticles themselves and the ligands they are coated with. To further improve the properties of the bidentate monozwitterionic ligand previously developed in our team, we synthesized a multidentate polyzwitterionic ligand, issued from the copolymerization of a bidentate monomer and a monozwitterionic one. The nanocrystals passivated by this polymeric ligand showed an exceptional colloidal stability, regardless of the medium conditions (pH, salinity, dilution, and biological environment), and we demonstrated the affinity of the polymer exceeded by 3 orders of magnitude that of the bidentate ligand (desorption rates assessed by a competition experiment). The synthesis of the multidentate polyzwitterionic ligand proved also to be easily tunable and allowed facile functionalization of the corresponding quantum dots, which led to successful specific biomolecules targeting.