An effective way to assemble partial views of a distributed system is to compute their product. Given two languages of message sequence charts generated by message sequence graphs, we address the problem of computing a message sequence graph that generates their product. Since all MSCs generated by a message sequence graph may be run within fixed bounds on the message channels, a subproblem is to decide whether the considered product is existentially bounded. We show that this question is undecidable but turns decidable in the restricted case where all shared events belong to the same process. For this case, we propose sufficient conditions under which a message sequence graph representing the product can be constructed.