This paper presents numerical simulations of transitions between back discharge regimes. Back discharge refers to any discharge initiated at or near a dielectric layer covering a passive electrode. In this work, a pinhole in a dielectric layer on a plane anode serves as a model for back discharge activity. We have studied transitions between back discharge regimes by varying the surface charge density on the dielectric layer and the electric field in front of the pinhole. From the variation of these two independent parameters, the back discharge regimes have been depicted as a mode diagram inspired by the experimental study of Masuda and Mizuno. The resulting diagram includes the different discharge regimes that are commonly observed in experiments. The propagation of a positive ionizing wave inside the pinhole toward its edge, and the resulting formation of a plasma zone at its exit constitute the onset stage of back discharge. From this stage, the transitions to volume discharge or surface discharge can occur. The volume discharge regime consists of the propagation of a discharge in space toward the cathode which can be superimposed with the propagation of a discharge above the dielectric layer surface. The diagram reveals the conditions for transitions between back discharge regimes.