I would advise you to not underestimate the enneagram's potential:
The original system was lacking to say the least. And did not come close to viable as a typological system until Katherine Fauvre tapped it's potential, who has successfully broke down the descriptions from vague characters archetypes to human attitudes, evolving enneagram into the system we now call tritype. In case by case experimentation, mixing sending people to reasonable tritype descriptions and deliberately misleading ones to others (even close ones), it has so far shows itself to be completely immune to the Forer effect - every description that isn't your own contains enough indication to break the need to identify with it - something none of the Jungian inspired typology systems can claim to do. Not quite having the massive room for metaphorical interpretation that Jungian functions deliver, it even has the potential to be the first system to pass the blind test.
The core axiom is that people gravitate towards fixed attitudes in the ways of deal with shame (2/3/4), anxiety (5/6/7) & anger (8/9/1), and developing defense mechanisms to deal with them. No one person can be defined by only one of those, but those defense mechanisms interact in certain ways that result in common attitudes. Unlike traditional MBTI or socionics, which deny the existence of certain function ordering, there is currently no assumption about which combinations might not be possible beyond that basic separation of heart head and gut types. Unfortunately, that means a fully flashed out version combining a tri-type of enneagram's with individual wings in a specific order and an instinctual variant would require 7,776 type profiles, and while Katherine gives a bit of a attention to the subtle differences in tritype ordering, someone taking the full scope of the endeavor has yet to have happened.