We study consistency conditions on a M(atrix) model which would describe M-theory on T 6 . We argue that there is a limit in moduli space for which it becomes a 6+1D theory and study the low-energy description of extended objects in the decompactified limit. We discuss the requirements from a M(atrix) model which would describe such an E 6 ( 6 ) theory. We suggest that it could be a 5+1D theory and that a 1+1D theory with (0,4) supersymmetry might be the M(atrix) model for the M(atrix) model of the E 6 ( 6 ) theory.