  Heavy neutrinos with additional interactions have recently been proposed as
an explanation to the MiniBooNE excess. These scenarios often rely on
marginally boosted particles to explain the excess angular spectrum, thus
predicting large rates at higher-energy neutrino-electron scattering
experiments. We place new constraints on this class of models based on
neutrino-electron scattering sideband measurements performed at MINER$\nu$A and
CHARM-II. A simultaneous explanation of the angular and energy distributions of
the MiniBooNE excess in terms of heavy neutrinos with light mediators is
severely constrained by our analysis. In general, high-energy neutrino-electron
scattering experiments provide strong constraints on explanations of the
MiniBooNE observation involving light mediators.
