Hi Kurt,
If in the VOL2 Lesson book and Workbook (Chapter1), you look over the composite fingerings, you’ll notice that they are in essence what many call 3 notes per string. All the techniques out there, whether it be C-A-G-E-D or 3 NPS, are encompassed by the heptatonic system. The heptatonic system is the most complete system! It is based on a mathematical foundation. People are just not seeing the big picture, because they have not been exposed to it, or are not organizing their understanding of scales on the fretboard in those terms! Others that have, don’t necessarily have a name for it. That said, most great players are “unknowingly” using a combination of C-A-G-E-D plus 2 overlapping fingerings (when playing vertically or in position), and 3 notes per string when moving horizontally across the fretboard. This may even be the case with your teacher if he is a good experienced jazz player.
It is my personal experience that using only one of these techniques exclusively will limit what you can play in several contexts. I say this because I was first a 3NPS guitarist, then discovered C-A-G-E-D, then the 2 additional fingerings, and ultimately was exposed to the big picture that encompasses everything!
If I can ever find the time, I’d like to post some videos slowing down solos of several great jazz guitarists, and pointing out measure by measure, how all their fingerings are included in the heptatonic system, regardless of what anyone may be calling it!