The structure of a series of highly Al-doped superconducting Y(RE)-123 (RE = rare earth element) single crystals was investigated by XRD and NMR methods. On the basis of the data obtained by the structural investigations combined with the studies of magnetic and optical properties, the formation of various superstructures in the samples of pseudo-tetragonal symmetry has been discussed. The correlation between the carrier concentration and T_c-values has been determined. The superconductivity (at 70 K) was indicated even at the 2/3 and 1/3 Al substitution for Cu in the basal and CuO₂ planes, respectively, in the phase presumably of a perovskite-like structural type.