This paper describes the mechanism underpinning modal staging behaviour in screeching jets. An upstream-propagating subsonic guided-jet mode is shown to be active in all stages of screech. Axial variation of shock-cell spacing manifests in the spectral domain as a series of suboptimal peaks. It is demonstrated that the guided-jet mode may be energized by interactions of the Kelvin–Helmholtz wavepacket with not only the primary shock wavenumber peak, but also suboptimal peaks; interaction with suboptimals is shown to be responsible for closing the resonance loop in multiple stages of jet screech. A consideration of the full spectral representation of the shocks reconciles several of the classical models and results for jet screech that had heretofore been paradoxical. It is demonstrated that there are multiple standing waves present in the near field of screeching jets, corresponding to the superposition of the various waves active in these jets. Multimodal behaviour is explored for jets in a range of conditions, demonstrating that multiple peaks in the frequency spectra can be due to either changes in which peak of the shock spectra the Kelvin–Helmholtz wavepacket is interacting with, or a change in azimuthal mode, or both. The absence of modal staging in high-aspect-ratio non-axisymmetric jets is also explained in the context of the aforementioned mechanism. The paper closes with a new proposed theory for frequency selection in screeching jets, based on the observation that these triadic interactions appear to underpin selection of the guided-jet mode wavelength in all measured cases.