Abstract: In this paper we investigate neutrino oscillations with altered dispersion relations in the presence of sterile neutrinos. Modified dispersion relations represent an agnostic way to parameterize new physics. Models of this type have been suggested to explain global neutrino oscillation data, including deviations from the standard three-neutrino paradigm as observed by a few experiments. We show that, unfortunately, in this type of models new tensions arise turning them incompatible with global data.