New measurements of the coherent elastic neutrino-nucleus scattering (CEvNS) are expected to be achieved in the near future by using two neutrino production channels with different energy distributions: the very low energy electron antineutrinos from reactor sources and the muon and electron neutrinos from spallation neutron sources (SNS) with a relatively higher energy. Although precise measurements of this reaction would allow an improved knowledge of standard and beyond the Standard Model physics, it is important to distinguish the different new contributions to the process. We illustrate this idea by constraining the average neutron root mean square (rms) radius of the scattering material, as a standard physics parameter, together with the nonstandard interactions (NSI) contribution as the new physics formalism. We show that the combination of experiments with different neutrino energy ranges could give place to more robust constraints on these parameters as long as the systematic errors are under control.