All your senses are constructed out of more basic sensory inputs and presented to the rest of your brain as higher-level abstractions. Hearing, for example, doesn't just present the raw noises being heard, but also yields a best-guess about the direction and distance of noise sources, and you can argue that the audio-location function should technically be a separate "sense".

Proprioception being an abstraction over touch and sight data that generates awareness of how your body is arranged in space is a sense in the same manner. And you can definitely get proprioception over more than your own body - partner dancers will quickly develop a felt sense of how their dance partner's body is moving, as well.