The term "MAX phase" refers to a very interesting and important class of layered ternary transition-metal carbides and nitrides with a novel combination of both metal and ceramic-like properties that have made these materials highly regarded candidates for numerous technological and engineering applications. Using (Cr2Hf)(2)Al3C3 as an example, we demonstrate the possibility of incorporating more types of elements into a MAX phase while maintaining the crystallinity, instead of creating solid solution phases. The crystal structure and elastic properties of MAX phase-like (Cr2Hf)(2)Al3C3 are studied using the Vienna ab initio Simulation Package. Unlike MAX phases with a hexagonal symmetry (P6(3)/mmc, #194), (Cr2Hf)(2)Al3C3 crystallizes in the monoclinic space group of P2(1)/m (#11) with lattice parameters of a = 5.1739 angstrom, b = 5.1974 angstrom, c = 12.8019 angstrom; alpha = beta = 90 degrees, gamma = 119.8509 degrees. Its structure is found to be energetically much more favorable with an energy (per formula unit) of -102.11 eV, significantly lower than those of the allotropic segregation (-100.05 eV) and solid solution (-100.13 eV) phases. Calculations using a stress versus strain approach and the VRH approximation for polycrystals also show that (Cr2Hf)(2)Al3C3 has outstanding elastic moduli.