I couldn't find notations for partner dances, however designing notations for contacts shouldn't be difficult. Notations for lead and follow more so. It depend

I couldn't find notations for partner dances, however designing notations for contacts shouldn't be difficult. Notations for lead and follow more so. It depends how far you want to go down the rabbit hole. For example, in ballroom, there is also a well-established way that formal technique is documented in books. For each step within a figure, it specifies in considerable detail things like which part(s) of the foot you’ll step on (heel then toe, for example), which way that foot will be pointing (roughly speaking using compass points), how the upper body will rotate relative to the lower body, and what kind of rise and fall you have through the legs and feet. There is a whole system of teaching and examinations based on this technique, and consequently most teachers really will teach the same basic technique to a beginner learning the same figure in their classes. Of course, this is very useful for a social style where people might dance with someone else from another school the next day! However, even in the standard technique books with all their detailed notation, that systematic approach doesn’t tell the whole story. There are often notes on how to dance some figures that explain details not captured effectively by the formal notation. Then, once you go beyond the basic technique and standard syllabus figures that almost everyone learns, as with many activities you find that performers and teachers develop their own styles and their own personal ways of explaining more advanced technical points. At that stage, even though the actions you’re talking about are usually consistent with the traditional technique, there is still a lot of scope for interpretation. So, I doubt you could ever have a systematic notation that captures all the subtleties of the actions that set apart a world champion from a quarter-finalist. It would take more than a lifetime of study, and by then the art would have evolved anyway.