Actually Melancholics really describes me, not my more favorable traits mind you, but yes, I have been know by my Melancholy. However, that is not the entirety of me. Its a gross disproportion based on observations from a skewed or bias view point.
I see why though that the groupings are SJ, SP, NF, NT, because its less on cognitive and more on communication. It would make more sense to break down types by SJ, SP, NJ, NP for cognitive. For actions it would probably be best to break down the types as FJ, FP, TJ, TP, but those groupings would not necessarily communicate the best.
You could also break types into four groups of functions:
FeTi-SiNe- ENTP, ESFJ, INTP, ISFJ
FeTi-SeNi- ESTP, ENFJ, ISTP, INFJ
TeFi-NeSi- ESTJ, ENFP, INFP, ISTJ
TeFi-NiSe- ENTJ, ESFP, ISFP, INTJ
I do not know it would serve as any purpose though, cause these types my not get along so well.