Electromagnetic scattering on subwavelength structures is attracting much attention owing to the broad range of possible applications where this phenomenon can be used. Fundamental limits of the scattering cross section, which are well understood in spherical geometries, are overlooked in cases of low-symmetry resonators. Here we revise the notion of superscattering and link this property with symmetry groups of scattering potentials. We demonstrate pathways to spectrally overlap several eigenmodes of a resonator in a way such that they interfere constructively and increase the scattering cross section. As a particular example, we demonstrate spectral overlapping of several electric and magnetic modes in a subwavelength ceramic resonator. The optimized structures have a dipolar scattering cross-section limit exceeding that for a sphere by up to a factor of 4. The revealed rules, which link symmetry groups with fundamental scattering limits, allow assessment of the designs and performance of subwavelength superscatterers, which can be used in label-free imaging, compact antennas, long-range radio-frequency identification, and many other fields.