We address what it means to "engage in a relationship" and suggest Social Breathing as a model of immersing ourselves in the metaphorical social air around us, which is necessary for shared intention and joint action. We emphasize how emergent properties of social systems arise, such as the shared culture of groups, which cannot be reduced to the individuals involved. We argue that the processes involved in Social Breathing are: (1) automatic, (2) implicit, (3) temporal, (4) in the form of mutual bi-directional interwoven exchanges between social partners and (5) embodied in the coordination of the brains and behaviors of social partners. We summarize cross-disciplinary evidence suggesting that these processes involve a multi-person whole-brain-body network which is critical for the development of both we-ness and relational skills. We propose that Social Breathing depends on each individual's ability to sustain multimodal interwovenness, thus providing a theoretical link between social neuroscience and relational/multi-person psychology. We discuss how the model could guide research on autism, relationships, and psychotherapy.