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Abstract Oxides with a face-centred cubic (fcc) anion sublattice are generally not considered as solid-state electrolytes as the structural framework is thought to be unfavourable for lithium (Li) superionic conduction. Here we demonstrate Li superionic conductivity in fcc-type oxides in which face-sharing Li configurations have been created through cation over-stoichiometry in rocksalt-type lattices via excess Li. We find that the face-sharing Li configurations create a novel spinel with unconventional stoichiometry and raise the energy of Li, thereby promoting fast Li-ion conduction. The over-stoichiometric Li–In–Sn–O compound exhibits a total Li superionic conductivity of 3.38 × 10⁻⁴ S cm⁻¹at room temperature with a low migration barrier of 255 meV. Our work unlocks the potential of designing Li superionic conductors in a prototypical structural framework with vast chemical flexibility, providing fertile ground for discovering new solid-state electrolytes.