You're getting this use of "coordinate system" from the STC, right?  This is yet another example of "coordinate system" being an overloaded term: the STC (I believe) means it to be something like "multiple coordinate frames mixed together to create a higher dimensional space" - that is a "system of coordinates" in the same sense of the word as a "system of equations".  But that's *not* the common usage of "coordinate system" meaning something like equatorial J2000 ir whatever.  So I think we would want to try to use different terminology here. (some possible, admittedly not great, ideas: `MultiFrame`, `SystemOfFrames`, or `MultiDimCoordinates`)