Nanoparticles functionalized with multiple ligands can be programmed to bind biological targets depending on the receptors they express, providing a general mechanism exploited in various technologies, from selective drug-delivery to biosensing. For binding to be highly selective, ligands should exclusively interact with specific targeted receptors, because formation of bonds with other, untargeted ones would lead to non-specific binding and potentially harmful behaviour. This poses a particular problem for multivalent nanoparticles, because even very weak bonds can collectively lead to strong binding. A statistical mechanical model is used here to describe how competition between different receptors together with multivalent effects can be harnessed to design ligand-functionalized nanoparticles insensitive to the presence of untargeted receptors, preventing non-specific binding.