A general formulation for controlling the external scattering coefficients of cylindrical harmonics is presented, generalizing previous results for cloaking of a bare dielectric particle. By inserting a suitable surface admittance at the boundary between a dielectric body and the background region, cylindrical harmonic waves can be enhanced by tailoring the admittance value. Two separate limiting cases for super-scattering features are presented and compared against the same bare particle reference case, providing insights on how to enhance the multi-harmonic scattering pattern. Using this formulation, super-scattering systems can be created, which are suitable for future implementation using active or passive thin metasurfaces.