To my mind, if we are called by Christ to be unified as a single body (1 Corinthians 12:11-14), then we are to bring Christ to every member no matter where they are. If that means going to someone's home and having communion with them there then praise be to God that we can bring the Body together. Communion is then an act of inclusion. Conversely, it could be argued that "private" Communion occurs when churches take the act of public Communion and restrict it beyond what the Scripture allows. In this case Communion becomes an act of exclusion and it divides the Body.