We investigate here, mainly from the point of view of the hierarchies generated by different classes of systems, two variants of the parallel communicating grammar systems (PCGS) with communication by command: the multiple and, respectively, the single communication case. We show that the hierarchies for regular and linear components collapse in the single communication case and the hierarchy for context-sensitive components collapses in both multiple and single communication cases. By a result in [3], it will follow from our result on systems with context-sensitive components that also the hierarchy for context-free components collapses in both cases. Some open problems are also formulated.