Neutrinos might interact among themselves through forces that have so far remained hidden. Throughout the history of the Universe, such secret interactions could lead to scatterings between the neutrinos from supernova explosions and the nonrelativistic relic neutrinos left over from the big bang. Such scatterings can boost the cosmic neutrino background () to energies of , making it, in principle, observable in experiments searching for the diffuse supernova neutrino background. Assuming a model-independent, but flavor universal, four-Fermi interaction, we determine the upscattered cosmic neutrino flux, and derive constraints on such secret interactions from the latest results from Super-Kamiokande. Furthermore, we also study prospects for detection of the boosted flux in future lead-based coherent elastic neutrino-nucleus scattering experiments. Nevertheless, given current constraints on flavor universal self-interactions, we find that the upscattered contribution to the total DSNB flux is negligible, making a possible measurement of the boosted insurmountable.