Are there churches A, B, and C, such that A is in full communion with B, B is in full communion with C, but A and C are not in full communion?

Or, in mathematical terminology, is the relationship of full communion a transitive relation ? I can easily imagine a scenario where church A is stricter in their rules for full communion than church B, but not so strict as to exclude B from full communion on those grounds. However, since B is more lenient, they have full communion with C, which is outside the bounds for church A. While that's easily imaginable, I don't know of any example of three church institutions where this is the case. Do any exist? Does communing with C create any tension in the relationship between B and A?