  We extend our earlier work by demonstrating how to construct classical string
solutions describing arbitrary superpositions of scattering and bound states of
dyonic giant magnons on S^5 using the dressing method for the SU(4)/Sp(2) coset
model. We present a particular scattering solution which generalizes solutions
found in hep-th/0607009 and hep-th/0607044 to the case of arbitrary magnon
momenta. We compute the classical time delay for the scattering of two dyonic
magnons carrying angular momenta with arbitrary relative orientation on the
S^5.
