The development of multi-doped oxides based on the La0.6Sr0.4Co0.2Fe0.8O3–δ (LSCF) and La1–xSrxMnO3+δ perovskites would help to achieve the improved electrochemical activity of air electrodes in protonic ceramic cells due to the formation of the single-phase triple-conducting material. The search for prospective medium-entropy and high-entropy oxides based on (La,Sr)(Co,Fe,Mn)O3–δ could provide the electrode material with advanced hydration ability. In the present work, the formation and stability of new La0.6Sr0.4CoxFe1–x–yMnyO3–δ phases are estimated by thermodynamic calculations and the structure factors. Experimentally obtained La0.6Sr0.4CoxFe1–x–yMnyO3–δ powder samples are characterized by X-ray and neutron powder diffraction. The refined crystal structure parameters of the medium-entropy single-phase La0.6Sr0.4Co0.33Fe0.33Mn0.33O3–δ (LSCFM333) oxide with the trigonal structure (space group R3‾c) and the cell parameters of a = 5.4642(1) Å and c = 13.284(4) Å in hexagonal axes are used to design of a supercell simulation for density functional theory (DFT) calculations. The first-principles results are proposed to evaluate the thermodynamic parameters of proton uptake to assess future applications of Mn-doped LSCF in proton-conducting ceramic cells. The calculated values of the hydration enthalpy ΔHhydr for the LSCF and LSCFM333 derivatives are equal to 4.5 kJ mol−1 and –3.5 kJ mol−1, respectively, which are supported by the thermogravimetric analysis (TGA). The present study shows that the modeling techniques, including the thermodynamic and DFT calculations, can be successfully applied to the design of the related oxide materials for applications in solid oxide cells.