Resonant excitation of multi-photon transitions in one-atom cavity QED, from the ground state to an excited dressed state, induce an additional semiclassical Rabi splitting. This "dressing of the dressed states" arises from a multi-photon blockade, where, for sufficiently strong coupling, detunings, brought about by the root n nonlinearity of the Jaynes-Cummings model, inhibit absorption of additional photons. We show how this behavior is revealed in the spectrum and photon correlations of the quasi-elastically scattered light. Explicit results are presented for the two-photon case. (C) 2009 Elsevier B.V. All rights reserved.