Solar wind speed plays an important role in the study of space weather prediction. Some workers have used it for measuring the arrival time of solar disturbances at 1 AU. The purpose of this work is to extend our previous study (Wu et al., 2005c) of some Halloween 2003 events by presenting additional physical effects of multiple shock interactions on the solar wind profile during a complex compound event. In order to achieve this goal, we track a group of specific solar events' plasma and magnetic field output as they propagate into interplanetary space. A one-dimensional, time-dependent adaptive grid MHD code is used to study the evolution and interaction of shocks from Sun through the heliosphere. The MHD simulation results demonstrate that the solar wind speed might increase about ≈25% after two shocks collide with each other. This kind of interaction can affect the accuracy of the identification of the solar source that causes the interplanetary event (e.g., magnetic cloud, coronal mass ejection, interplanetary shock, or some other interplanetary discontinuity.) In this study we further simulate part of the famous Halloween 2003 events that contain at least four major solar events (flares) during 28 October to 1 November 2003. These major events, simulated by pressure pulses, generated shocks that matched well with ACE (Advanced Composition Explorer) observations as reported by Wu et al. (2005c) in our previous study. The present work presents new details concerning the interplay (such as sunward and antisunward traveling compression and rarefaction waves) between fast forward and fast reverse interplanetary shocks.