The respiratory rhythm and motor pattern are hypothesized to be generated by a brain stem respiratory network with a rhythmogenic core consisting of neural populations interacting within and between the pre-Bötzinger (pre-BötC) and Bötzinger (BötC) complexes and controlled by drives from other brain stem compartments. Our previous large-scale computational model reproduced the behavior of this network under many different conditions but did not consider neural oscillations that were proposed to emerge within the retrotrapezoid nucleus/parafacial respiratory group (RTN/pFRG) and drive preinspiratory (or late-expiratory, late-E) discharges in the abdominal motor output. Here we extend the analysis of our previously published data and consider new data on the generation of abdominal late-E activity as the basis for extending our computational model. The extended model incorporates an additional late-E population in RTN/pFRG, representing a source of late-E oscillatory activity. In the proposed model, under normal metabolic conditions, this RTN/pFRG oscillator is inhibited by BötC/pre-BötC circuits, and the late-E oscillations can be released by either hypercapnia-evoked activation of RTN/pFRG or by hypoxia-dependent suppression of RTN/pFRG inhibition by BötC/pre-BötC. The proposed interactions between BötC/pre-BötC and RTN/pFRG allow the model to reproduce several experimentally observed behaviors, including quantal acceleration of abdominal late-E oscillations with progressive hypercapnia and quantal slowing of phrenic activity with progressive suppression of pre-BötC excitability, as well as to predict a release of late-E oscillations by disinhibition of RTN/pFRG under normal conditions. The extended model proposes mechanistic explanations for the emergence of RTN/pFRG oscillations and their interaction with the brain stem respiratory network.