We consider a particular effect which can be expected in scenarios of deviations from Special Relativity induced by Planckian physics: the loss of additivity in the total energy of a system of particles. We argue about the necessity to introduce a length scale to control the effects of non-additivity for macroscopic objects and consider white dwarfs as an appropriate laboratory to test this kind of new physics. We study the sensitivity of the mass-radius relation of the Chandrasekhar model to these corrections by comparing the output of a simple phenomenological model to observational data of white dwarfs. ; Comment: 13 pages, 3 figures