Wave scattering from a cylinder with a tensor impedance surface is investigated based on the Lorentz-Mie theory. A practical example of such a cylinder is a subwavelength metallic rod with helical dielectric-filled corrugations. The investigation is performed with the aim to maximize scattering cross-section by tailoring the surface impedance of cylindrical scatterers. For the normally incident TEz and TMz waves the required surface impedance of a subwavelength cylinder can be produced by longitudinal (axial) and transverse (circumferential) corrugations, respectively. It is shown that such corrugations induce superscattering at multiple frequencies, which can be widely tuned with either or both the size and permittivity of dielectric-filled corrugations. In the microwave band, this effect is demonstrated to be robust to material losses and is validated against the fullwave simulations and experiment. For the TEz waves the enhanced scattering from the cylinder is found to have a broad frequency bandwidth, provided that the relative permittivity of corrugations is low or equal unity. In the latter case, the corrugated cylinder acts as an all-metal superscatterer. For such cylinders the near-field measurements are implemented and provide the first experimental evidence of the superscattering phenomenon for all-metal objects. In addition to multifrequency superscattering, the dielectric-filled corrugations are shown to provide multifrequency cloaking of the cylinder under the incidence of the TMz waves. Simultaneous superscattering and cloaking at multiple frequencies distinguishes corrugated cylinders from other known practicable scatterers for potential applications in antenna designing, sensing, and energy harvesting.Enhancement of wave scattering from small objects is a vital issue in present-day technologies [1-7], including miniaturized antennas, sensors and energy harvesting devices. This issue is directly related to the natural constraint inherent in most subwavelength scatterers [8]. This constraint is known as a single-channel limit [9], which represents an upper limit to scattering crosssection for such scatterers and is attained under resonance condition for one of the scattering modes (channels). The only way to overcome this constraint is to ensure resonant scattering of several modes at a single frequency. Such a resonance overlapping magnifies scattering from a given object and is known as superscattering [9,10]. The larger the number of resonant modes, the larger the superscattering cross-section. Therefore, theoretically, superscattering opens a way to arbitrary enhancement of wave scattering from subwavelength objects. In practice, however, this effect is often hindered by the lack of low-loss materials and appropriate design solutions.In the infrared and visible parts of spectrum, the superscattering can be realized in cylindrical structures formed by several plasmonic and dielectric layers. In the pioneering work [9], for such a structure the total scattering cross-section was optimized to excee...