In this work we explore the rheology of very concentrated (0.55<Φ<0.67) suspensions of carbonyl iron (CI) particles coated by a small polymer. A strong DST is observed in a large range of volume fraction presenting some specificities relatively to other systems. In particular, in a given range of volume fraction, the DST transition appears suddenly without being preceded by shear thickening. The presence of a frictional network of particles is confirmed by a simultaneous measurement of the electric resistance of the suspension and of the rheological curve. Using the Wyart-Cates model we show that, increasing the volume fraction, the fraction of frictional contacts grows more and more quickly with the stress that disagrees with the prediction of computer simulations. The same kind of behavior is observed in the presence of a magnetic field with, in addition, a very strong increase of the viscosity with the magnetic field before the transition. We interpret this behavior by the interpenetration of the polymer layer under the effect of the shear stress-and of the magnetic stress-followed by the expulsion of the polymer out of the surfaces. Besides we point that, above the DST transition, we do not observe a jamming in the range of volume fraction whereas it is predicted by the W-C model. Based on the fact that in the absence of shear flow, the polymer should come back to the surface and destroy the frictional contacts we can predict an asymptotic non-zero shear rate and reproduce the experimental behavior.