  We perform microscopic calculations of the inelastic cross sections for the
double and triple excitation of giant resonances induced by heavy ion probes
within a semicalssical coupled channels formalism. The channels are defined as
eigenstates of a bosonic quartic Hamiltonian constructed in terms of collective
RPA phonons. Therefore, they are superpositions of several multiphonon states,
also with different numbers of phonons and the spectrum is anharmonic. The
inclusion of (n+1) phonon configurations affects the states whose main
component is a n-phonon one and leads to an appreacible lowering of their
energies. We check the effects of such further anharmonicities on the previous
published results for the cross section for the double excitation of Giant
Resonances. We find that the only effect is a shift of the peaks towards lower
energies, the double GR cross section being not modified by the explicity
inclusion of the three-phonon channels in the dynamical calculations. The
latters give an important contribution to the cross section in the triple GR
energy region which however is still smaller than the experimental available
data. The inclusion of four phonon configurations in the structure calculations
does not modify the results.
