Converts 2-oxo acids to branched-chain amino acids. Acts on leucine, isoleucine and valine. Also involved in methionine chain elongation cycle of aliphatic glucosinolate formation. Catalyzes the conversion of 5-methylthiopentyl-2-oxo and 6-methylthiohexyl-2-oxo acids to their respective Met derivatives, homomethionine and dihomo-methionine, respectively