In a mesoscale convective system (MCS), convection that redevelops over (i.e., back-builds), and/or repeatedly passes over (i.e., trains) a region for an extended period of time can contribute to extreme rainfall and flash flooding. Past studies have indicated that both mesoscale ascent and lifting of the inflow layer by a cold pool or bore are important when this back-building/training convection is displaced from the leading line [sometimes called rearward off-boundary development (ROD)]. However, Plains Elevated Convection At Night (PECAN) field campaign observations suggest that the stability of the nocturnal boundary layer is highly variable and some MCSs with ROD have only a weak surface cold pool. Numerical simulations presented in this study suggest that in an environment with strong boundary layer stability, ROD can be supported by mechanisms other than those mentioned above. Simulations were initialized using a sounding from ahead of a PECAN MCS with a strong stable layer and ROD, and the three-dimensional simulation produced an MCS similar to that observed despite the homogeneous initial conditions. Some of the findings presented herein challenge existing understanding of nocturnal MCSs, and especially how downdrafts interact with a stable boundary layer. Notably, downdrafts can reach the surface, and different regions of the MCS may have different propagation mechanisms and different relevant inflow layers. Unlike previous studies of ROD, parcel lifting may be supported by an intrusion (an elevated layer of downdraft air) modified by the three-dimensional vertical wind shear.