I was looking for the same thing, specifically for 3, and came across trinaltrinal. (For example, the aeroplane had dual controls.)
Re above suggestions: triple and three-fold have the connotation of identical instances or a multiplication of a single instance, which dual does not. (They also have the limitation of being related to double and twofold.) Three-way has connotations of some sort of physical object or direction, that I don't want either. Triadic might work but it is of Greek origin, whereas dual and trinal are from Latin.
Paucal, is not specific to three, but is a good alternative to multiple.