jats:titleAjats:scbstract</jats:sc> </jats:title>jats:pCanonical neutrino oscillations arise due to the propagation of three mass eigenstates from production to detection. We aspire to capture, in one simple framework, a broad range of new physics effects on neutrino propagation beyond this canonical picture — this can be done by promoting the neutrino propagators to the general Källén-Lehmann form. In this work we demonstrate how models predicting additional light propagating species of neutrino are naturally accommodated in this language and propose a simple model spectrum composed of just three ‘broadened’ states as a flexible ansatz by which to explore the phenomenology of new physics in neutrino propagation. Reinterpreting existing neutrino oscillation measurements, we illustrate how this framework provides the capacity to probe deviations from the standard three-neutrino scenario systematically and generally. Whilst current data allows for relatively strong constraints on broadened neutrinos, we find the upcoming JUNO experiment will yield significant improvements, particularly for the heaviest neutrino, paving the way to a clearer understanding of how neutrinos propagate in vacuum.</jats:p>