Using the exact Muffin-Tin orbital method combined with the coherent potential approximation, the effects of magnetic disordering and alloying effects on the phase stability of L2 ₁- and D0 ₂₂-Co ₂Cr Z( Z= Ga, Si, Ge) alloys are systematically investigated at 0 K in the present work. It is shown that at 0 K, the lattice parameter, bulk modulus, magnetic moments, and elastic constants of the studied L2 ₁alloys are in line with the available theoretical and experimental data. In the ferromagnetic state, these alloys possess L2 ₁structure; with the magnetic disordering degree ( y) increasing, the energy of the phase increases relatively and finally turns from lower than D0 ₂₂phase to higher than D0 ₂₂phase. As a result, when y≥ 0.1 (0.2), then Z= Si and Ge ( Z= Ga) alloys are stabilized by the D0 ₂₂phase. With yincreasing, the tetragonal shear elastic modulus ( C '= ( C ₁₁– C ₁₂)/2) also turns soft, indicating that the magnetic disorderingis conducive to the lattice tetragonal deformation in the three alloys from both the energetic view and the mechanical view. The electronic origination of the magnetic disordering effect on the stabilities of the L2 ₁and D0 ₂₂phases can be ascribed to the Jahn-Teller instability effect. In the FM L2 ₁-Co ₂CrGa _1–xSi _xand L2 ₁-Co ₂CrGa _1–xGe _xquaternary alloys, with xincreasing, the total magnetic moment increases monotonically according to the Slater-Pauling rule, and C 'also stiffens, reflecting that the adding of Si and Ge can promote the mechanical stability of L2 ₁-Co ₂CrGa alloy, thereby depressing the lattice tetragonal deformation.