  We address the problem of studying the decay of the inflaton field $\phi$ to
another scalar field $\chi$ through parametric resonance in the case of a
coupling that involves several decay modes. This amounts to the presence of
extra harmonic terms in the perturbation of the $\chi$ field dynamics. For the
case of two frequencies we compute the geometry of the resonance regions, which
is significantly altered due to the presence of non-cuspidal resonance regions
associated to higher harmonics and to the emergence of instability `pockets'.
We discuss the effect of this change in the efficiency of the energy transfer
process for the simplest case of a coupling given by a combination of the two
interaction terms of homogeneous degree usually considered in the literature.
We find that the presence of higher harmonics has limited cosmological
implications.
