Advances in solid-state batteries have primarily been driven by the discovery of superionic conducting structural frameworks that function as solid electrolytes. We demonstrate the ability of high-entropy metal cation mixes to improve ionic conductivity in a compound, which leads to less reliance on specific chemistries and enhanced synthesizability. The local distortions introduced into high-entropy materials give rise to an overlapping distribution of site energies for the alkali ions so that they can percolate with low activation energy. Experiments verify that high entropy leads to orders-of-magnitude higher ionic conductivities in lithium (Li)-sodium (Na) superionic conductor (Li-NASICON), sodium NASICON (Na-NASICON), and Li-garnet structures, even at fixed alkali content. We provide insight into selecting the optimal distortion and designing high-entropy superionic conductors across the vast compositional space.