Multipoint communication - simultaneous transmission from multiple sources to a group of receivers - has numerous applications on Internet. However, the problem is mainly studied in the domain of multicasting for a group involving a single source, restricting the consideration of multiple sources to the performance analysis of the proposed solutions. Furthermore, existing protocols in the literature only consider as a design issue a single metric, and mostly operate without regarding a delay constraint. In this paper, we examine the multiple-source delay-constrained multipoint communication problem with dynamic membership. We characterize potential solutions, and show that expanding the solution space to include more efficient solutions can enhance the development of delay-constrained multipoint paths.