The phenomenon of discontinuous shear thickening (DST) is observed in suspensions of solid particles with a very high-volume fraction. For suspensions of ferromagnetic particles this transition can also be triggered by the application of a magnetic field (Bossis et al. 2016). Here we explore the rheological behavior of a bidisperse suspension made of magnetic -carbonyl iron(CI)- and non-magnetic -calcium carbonate (CC)- particles with a brush like coating of the same superplasticizer molecule. We highlight the synergetic effect of non-magnetic particles whose inclusion in the percolated frictional network amplifies the effect of the magnetic field on the remaining fraction of magnetic particles. In plate-plate geometry, a small fraction of ferromagnetic particles (about 5%) is sufficient to trigger the transition by the application of a magnetic field and optimum for the increase of viscosity. The progressive interpenetration of the coating layers of polymer and the demagnetizing field can explain this behavior.