We study the sensitivity of JUNO and TAO to the oscillations induced by two well-motivated scenarios beyond the standard model: large extra dimensions (LEDs) and light sterile neutrinos in the context of 3+1 neutrino mixing. We find that JUNO+TAO can set competitive bounds on the parameter space of each scenario. In particular, we find that JUNO+TAO can be competitive with MINOS, DUNE, or KATRIN in the context of LED. If LEDs are present in nature, we show that the parameters could be measured with a similar precision as the standard oscillation parameters. We also show that JUNO+TAO can test nearly all of the parameter space preferred by gallium experiments in the context of 3+1 mixing. Finally, we discuss the possibility to distinguish the two scenarios from each other.