We present the consequences of a large radiative correction term coming from Supersymmetry (SUSY) upon the electron neutrino fluxes streaming off a core-collapse supernova using a 3-flavour neutrino-neutrino interaction code. We explore the interplay between the neutrino-neutrino interaction and the effects of the resonance associated with the μ−τ neutrino index of refraction. We find that sizeable effects may be visible in the flux on Earth and, consequently, on the number of events upon the energy signal of electron neutrinos in a liquid argon detector. Such effects could lead to a probe for Beyond Standard Model (BSM) physics and, ideally, to constraints in the SUSY parameter space.