All-dielectric nanophotonics opens a venue for a variety of novel phenomena and scattering regimes driven by unique optical effects in semiconductor and dielectric nanoresonators. Their peculiar optical signatures enabled by simultaneous electric and magnetic responses in the visible range pave a way for a plenty of new applications in nano-optics, biology, sensing, etc. In this work, we investigate fabrication-friendly truncated cone resonators and achieve several important scattering regimes due to the inherent property of cones—broken symmetry along the main axis without involving complex geometries or structured beams. We show this symmetry breaking to deliver various kinds of Kerker effects (generalized and transverse Kerker effects), non-scattering hybrid anapole regime (simultaneous anapole conditions for all the multipoles in a particle leading to the nearly full scattering suppression) and, vice versa, superscattering regime. Being governed by the same straightforward geometrical paradigm, discussed effects could greatly simplify the manufacturing process of photonic devices with different functionalities. Moreover, the additional degrees of freedom driven by the conicity open new horizons to tailor light-matter interactions at the nanoscale.