The radiative heat transfer between two dielectrics can be strongly enhanced in the near field in the presence of surface phonon-polariton resonances. Nevertheless, the spectral mismatch between the surface modes supported by two dissimilar materials is responsible for a dramatic reduction of the radiative heat flux they exchange. In the present paper we study how the presence of a graphene sheet, deposited on the material supporting the surfacewave of lowest frequency, allows us to widely tune the radiative heat transfer, producing an amplification factor going up to one order of magnitude. By analyzing the Landauer energy transmission coefficients we demonstratethat this amplification results from the interplay between the delocalized plasmon supported by graphene and the surface polaritons of the two dielectrics. We finally show that the effect we highlight is robust with respect to the frequency mismatch, paving the way to an active tuning and amplification of near-field radiative heat transfer in different configurations.