But it sounds like a free standing temperament matrix in its own right. The factors sound almost similar to Interaction Styles; (which are not free-standing, but interwoven into the type code).
I can't recall there being any subtypes in MBTI. There exist subtypes in socionics. These subtypes are based on the strength of your dominant vs your auxiliary function. For instance for ESFP there are two subtypes, the Fi-ESFP and the Se-ESFP, and so it goes for all the other type as well.
Subtype Descriptions by V. Meged, A. Ovcharov
Technically, MBTI doesn't have subtypes like Enneagram and Socionics (Big 5 doesn't have any subtypes either), just preference strength. However, if MBTI is combined with Enneagram or the Big 5, it can make MBTI look as if there were subtypes.
Thinkist: not optimist nor pessimist. I am primarily competent in the enneagram.
SX 9w1, SP 5w6, SP 3w4 | Split with the first two
Ti-Se-Si-Ni-Te-Fi-Ne-Fe. I'm always questioning this, particularly the Si.
Big 5/Global5/SLOAN: RCUEX