Binder compositions are described, where the compositions include a protein, a first crosslinking compound that includes a carbohydrate, and a second crosslinking compound that includes two or more primary amine groups. The first and second crosslinking compounds may be individually crosslinkable with each other and with the protein. Also described are fiber products that may include inorganic or organic fibers and a cured thermoset binder prepared from a protein and at least two crosslinking compounds. Additionally, methods of making fiber products are described that include providing inorganic or organic fibers, and applying a liquid binder composition to the fibers to form a fiber-binder amalgam. The liquid binder composition may include a protein and at least two crosslinking compounds that include a carbohydrate and an organic amine with two or more primary amines. The amalgam may be heated to a curing temperature to form the fiber product.