In this study, we present a general-purpose methodology for deriving the three-dimensional (3D) arrangement of multivalent transmembrane complexes in the presence of their ligands. Specifically, we predict the most likely families of structures of the experimentally intractable trimeric asialoglycoprotein receptor (ASGP-R), which consists of human hepatic subunits (two subunits of H1 and one subunit of H2), bound to a triantennary oligosaccharide (TA). Because of the complex nature of this multivalent type-II transmembrane hetero-oligomeric receptor, structural studies have to date been unable to provide the 3D arrangement of these subunits. Our approach is based on using the three-pronged ligand of ASGP-R as a computational probe to derive the 3D conformation of the complex and then using this information to predict the relative arrangement of the protein subunits on the cell surface. Because of interprotein subunit clashes, only a few families of TA conformers are compatible with the trimeric structure of ASGP-R. We find that TA displays significant flexibility, matching that detected previously in FRET experiments, and that the predicted complexes derived from the viable TA structures are asymmetric. Significant variation exists with respect to TA presentation to the receptor complex. In summary, this study provides detailed information about TA-ASGP-R interactions and the symmetry of the complex.