A coalitional matching is a two-sided matching problem in which agents on each side of the market may form coalitions such as student groups and research teams who - when matched - form universities. We assume that each researcher has preferences over the research teams he would like to work in and over the student groups he would like to teach to. Correspondingly, each student has preferences over the groups of students he wants to study with and over the teams of researchers he would like to learn from. In this setup, we examine how the existence of core stable partitions on the distinct market sides, the restriction of agents' preferences over groups to strict orderings, and the extent to which individual preferences respect common rankings shape the existence of core stable coalitional matchings.