Superionic ice is a special group of ice phases at high temperature and pressure, which may exist in ice-rich planets and exoplanets. In superionic ice liquid hydrogen coexists with a crystalline oxygen sublattice. At high pressures, the properties of superionic ice are largely unknown. Here we report evidence that from 280 GPa to 1.3 TPa, there are several competing phases within the close-packed oxygen sublattice. At even higher pressure, the close-packed structure of the oxygen sublattice becomes unstable to a new unusual superionic phase in which the oxygen sublattice takes the P2(1)/c symmetry. We also discover that higher pressure phases have lower transition temperatures. The diffusive hydrogen in the P2(1)/c superionic phase shows strong anisotropic behaviour and forms a quasi-two-dimensional liquid. The ionic conductivity changes abruptly in the solid to close-packed superionic phase transition, but continuously in the solid to P2(1)/c superionic phase transition.