The present invention provides common ligand mimics that act as common ligands for a receptor family. The present invention also provides bi-ligands containing these common ligand mimics. Bi-ligands of the invention provide enhanced affinity and/or selectivity of ligand binding to a receptor or receptor family through the synergistic action of the common ligand mimic and specificity ligand that compose the bi-ligand. The present invention also provides combinatorial libraries containing the common ligand mimics and bi-ligands of the invention. Further, the present invention provides methods for manufacturing the common ligand mimics and bi-ligands of the invention and methods for assaying the combinatorial libraries of the invention.