A new silver iodide borate, Ag₃B₆O₁₀I, is presented as a promising solid-state electrolyte with a δ ↔ γ ↔ β ↔ α cascade of the isosymmetric superionic phase transitions. Its crystal structure is composed of two sublattices, the “host” B-O covalent part from B₆O₁₃ 6B:3Δ3□:[φ]<Δ2□>|<Δ2□>|<Δ2□>| corner-sharing hexaborate groups, and the “guest” Ag-I ionic part. The transitions are associated with structural re-arrangements of the latter with a stepwise “melting” of silver sublattice and give rise to an increase in conductivity to 0.005 S cm⁻¹ at 99 °C. Exceptionally large room-temperature anharmonicity of silver vibration has been described. The migration of silver ions leads to negative thermal expansion (NTE) at 25-400 °C. The sodium analog, Na₃B₆O₁₀I, with a “normal” perovskite-like structure was obtained. The structural diversity in the M₃B₆O₁₀X family can be rationalized considering the difference in the ionic radii of X⁻ anions and M⁺ cations.