Contrary to the usual belief that MHD intermediate shocks are extraneous, we have recently shown by numerical solutions of dissipative MHD equations that intermediate shocks are admissible and can be formed through nonlinear steepening from a continuous wave. In this paper, we clarify the differences between the conventional view and our results by studying the interaction of an MHD intermediate shock with an intermediate wave. The study reaffirms our results. In addition, the study shows that there exists a larger class of shocklike solutions in the time-dependent dissipative MHD equations than are given by the MHD Rankine-Hugoniot relations. It also suggests a mechanism for forming rotational discontinuities through the interaction of an intermediate shock with an intermediate wave. The results are of importance not only to the MHD shock theory but also to studies such as magnetic field reconnection models. ¿ American Geophysical Union 1988