When a charged particle interacts with an atom it may induce double electronic transitions. The complete information on such a reaction is encompassed in the Green function of the interacting four-particle system -the external charged particle, the two electrons, and the residual ion!. In this work we employ a perturbation expansion of the Green operator and derive from that a multiple-scattering series for the scattering operator. As pointed out here, each term in this series corresponds to a particular sequence of binary potential collisions. From a simple analytical analysis we identify the regions of the four-body spectrum where the effects of the multiple-scattering terms become prevalent. We uncover the existence of a left-right asymmetry in a two-particle collision. This dichroic feature occurs because the symmetry of space is broken by the presence of the particles not participating in the two-body encounter. We study the ionization-ionization-transfer reaction when the external charged particle is heavy. The present formal, exact analysis predicts, in addition to the Thomas peaks, a triple-star peak structure in the spectrum when considered as a function of the momenta of the ionized electron, the residual ion and the scattered projectile. It is shown that the star is two dimensional and that its shape is dependent on the velocity of the continuum electron. In addition we consider the ionization and positronium formation following the scattering of a positron from an atom. We point out that certain terms in the multiple-scattering series coincide due to the equal masses of the electron and the positron which open the way for interference effects.