Wegivenecessaryandsufficientconditionsonanm-isometrytohavean invertiblem-isometricalextension.Asparticularcases,wegiveausefulcharacterizationforageneralm-isometricalunilateralweightedshiftandforℓ-Jordanisometries. Inparticular, everyℓ-Jordanisometryoperatorhasaninvertible(2ℓ−1)-isometrical extension.