The collision integral cross sections are obtained and computed for several experimentally realizable cases to understand the various features of the higher-order process known as double photon Compton scattering. The computational work carried out using the Mathematica software package generally corresponds to three different incident gamma photon energies of 137Cs (661.65 keV), 65Zn (1.12 MeV), and that from the radiative capture of 19F (6.14 MeV). The characteristic features revealed a need to be investigated experimentally to check for their support to the currently acceptable theory of this quantum electrodynamics process. An experimental technique has been suggested for the measurement of these collision integral cross sections.