If you're asking about "communion" in the sense of two denominational groups being in communion with each other (so that, e.g., clergy from one denomination can serve in churches of the other denomination), that's going to be more restricted. The Lambeth Quadrilateral is a good starting point here. As summarized in the Wikipedia article:
- The Holy Scriptures, as containing all things necessary to salvation;
- The creeds (specifically, the Apostles' and Nicene Creeds), as the sufficient statement of Christian faith;
- The dominical sacraments of baptism and Holy Communion;
- The historic episcopate, locally adapted.
Most Christian groups value the Scriptures, the two listed creeds, and the two listed sacraments. Points of contention tend to be that some other groups want a lengthier list of creeds or confessions (we don't want to require any other creeds), and that many Christian groups don't try to preserve apostolic succession (which is important to us). If there was a policy in one group that barred recognition of the other group's clergy -- for example, if a group did not recognize our female Episcopal priests as being validly ordained -- then that would be a problem as well, due to the nature of what intercommunion is trying to achieve. An intercommunion agreement was negotiated with the ELCA some decades back, and I think talks are underway with the Methodists.