First-principles calculations were performed to investigate the elastic and thermodynamic properties for multi-component Co-based superalloy systems and explored the effect of alloying on stabilizing the γ′ phase. First, the comparisons were carried out for the γ′ phase in Co3(Al,TM) (TM being transition metals) and Ni3Al systems between the present computational results using the EMTO-CPA method and other available DFT calculations as well as experimental data. The lattice parameters, elastic constants, and Debye temperatures are consistent with experimental results and other calculations. The predicted thermodynamic properties, e.g., the Gibbs free energy, excess entropy, and linear thermal expansion coefficient, agree well with CALPHAD results, experimental results, and other available first-principles calculations. A combination of EMTO-CPA method and Debye–Grüneisen model is utilized in this work to ensure that the alloying effect on the stability of the γ′ phase in a multi-component Co-based system is captured efficiently. This could open the path for designing novel multi-component Co-based alloys based on first-principles calculation. To demonstrate this, predictions for the properties of multicomponent systems were undertaken. Our results show that Ni aids in the stabilization of the (CoNi)3(Al, Mo, Nb) phase. Graphical Abstract: [Figure not available: see fulltext.]