Multivalent antigen-binding proteins comprising two or three or four or more immunoglobulin heavy chain variable domain binding domains are provided, as are methods for making them, nucleic acid constructs, and cell lines for making them. Proteins comprising two or three or four or more different heavy chain variable domains that lack an immunoglobulin variable domain are provided. Proteins comprising two or three or four or more different heavy chain variable domains that associate with the same immunoglobulin light chain variable domain are also provided.