A genetically modified mouse is provided, wherein the mouse expresses an immunoglobulin light chain repertoire characterized by a limited number of light chain variable domains. Mice are provided that present a choice of two human light chain variable gene segments such that the immunoglobulin light chains expresses by the mouse comprise one of the two human light chain variable gene segments. Methods for making bispecific antibodies having universal light chains using mice as described herein, including human light chain variable regions, are provided. Methods for making human variable regions suitable for use in multispecific binding proteins, e.g., bispecific antibodies, and host cells are provided.