Phase stability, elastic, and thermodynamic properties of (Co,Ni)3(Al,Mo,Nb) with the L12 structure have been investigated by first-principles calculations. Calculated phonon density of states show that (Co,Ni)3(Al,Mo,Nb) is dynamically stable, and calculated elastic constants indicate that (Co,Ni)3(Al,Mo,Nb) possesses intrinsic ductility. Young’s and shear moduli of the simulated polycrystalline (Co,Ni)3(Al,Mo,Nb) phase are calculated using the Voigt–Reuss–Hill approach and are found to be smaller than those of Co3(Al,W). Calculated electronic density of states depicts covalent-like bonding existing in (Co,Ni)3(Al,Mo,Nb). Temperature-dependent thermodynamic properties of (Co,Ni)3(Al,Mo,Nb) can be described satisfactorily using the Debye–Grüneisen approach, including heat capacity, entropy, enthalpy, and linear thermal expansion coefficient. Predicted heat capacity, entropy, and linear thermal expansion coefficient of (Co,Ni)3(Al,Mo,Nb) show significant change as a function of temperature. Furthermore the obtained data can be used in the modeling of thermodynamic and mechanical properties of Co-based alloys to enable the design of high temperature alloys.