• Compositionally complex cobaltites with 3-8 lanthanides at the Ln-site were synthesized and classified as medium entropy oxides.
• All compounds crystallize in tetragonal double perovskite structure (P4/mmm), with lattice parameters governed by average ionic radius rather than configurational entropy.
• Oxygen non-stoichiometry is consistently higher than in low entropy counterparts, enhancing mixed ionic-electronic conductivity.
• Electrical conductivity exceeds 50 S/cm for all compositions, peaking at 1487 S/cm for BaLa1/3Nd1/3Gd1/3Co2O6−δ at 300°C, but decreases with increasing number of substituents.