This paper reports an extension of the Dead Space Multiplication Theory (DSMT) that enables determining the spatial distribution of the impact ionizations for arbitrary heterojunction multiplication regions. The newly developed recursive equations allow determination of the number of impact-ionization events triggered by electrons and holes in an arbitrary sub-region of the multiplication region. Moreover, the model can incorporate a relaxation mechanism for suppressing the impact ionizations triggered by one species of carrier. By numerically solving an extended set of recursive equations for carrier ionizations, the spatial distribution of impact ionization has been calculated for two different cases of the multiplication region: a hole-injection InP homojunction multiplication region; and an electron-injection InAlAs/InAlGaAs I2E multiplication region. The latter structure is designed so that it suppresses the hole-initiated ionizations by incorporating a hole relaxation mechanism via phonon scattering.