If pragmatics deal with how the extralinguistic environment affects the interpratation of an utterance, which branch of linguistics deals with how the paralinguistic environment affects the interpratation of an utterance?
An example of paralinguistic feature (maybe the most prominent) would be prosody.
An example of extralinguistic environment would be the situational/social context. I.e the fact that The 2 persons communicating are housemates.