Intercommune :: Intercommune (v. i.) To have mutual communication or intercourse by conservation.
Intercommunicate :: Intercommunicate (v. i.) To communicate mutually; to hold mutual communication.
Intercommunion :: Intercommunion (n.) Mutual communion; as, an intercommunion of deities..
Intercommunity :: Intercommunity (n.) Intercommunication; community of possessions, religion, etc..