We study the gravito-electromagnetic perturbations of the Kerr-Newman (KN) black hole and identify the two???photon sphere and near-horizon???families of quasinormal modes (QNMs) of the black hole, computing the frequency spectra (for all the KN parameter space) of the modes with the slowest decay rate. We uncover a novel phenomenon for QNMs that is unique to the KN system, namely eigenvalue repulsion between QNM families. Such a feature is common in solid state physics where e.g., it is responsible for energy bands/gaps in the spectra of electrons moving in certain Schr??dinger potentials. Exploiting the enhanced symmetries of the near-horizon limit of the near-extremal KN geometry, we also develop a matched asymptotic expansion that allows us to solve the perturbation problem using separation of variables and provides an excellent approximation to the KN QNM spectra near extremality. The KN QNM spectra derived here are needed not only to account for gravitational emission in astrophysical environments, such as the ones probed by LIGO, Virgo and LISA, but also to allow one to extract observational implications of several new physics scenarios, such as minicharged dark-matter or certain modified theories of gravity, whose observables degenerate to those of the KN solution at the scale of binary mergers.