Communication structured occurrence nets (csons) are the basic variant of structured occurrence nets which have been introduced to characterise the behaviours of complex evolving systems. A cson has the capability of portraying different types of interaction between systems by using special elements to link with multiple (component) occurrence nets. Communication structured place transition nets (cspt-nets) are the system-level counterpart of csons. In this paper, we investigate cspt-nets unfoldings containing representations of all the single runs of the original nets captured by csons. We develop several useful notions related to cspt-net unfoldings, and then present an algorithm for constructing the new class of unfolding.