I think that what a personality system is ideally trying to accomplish is to discover the basic archetypes or themes that personalities can take on. What I have noticed is that, with respect to the Enneagram, Socionics, and the MBTI, there are certain themes in each system. The themes overlap, but there are some themes that are captured better in certain systems, and some themes that are not captured at all in others.
For example, let's consider the four "Researcher" types in Socionics:
The Researcher types take on the following roles:
ENTp - Inventor
INTp - Observer/Critic
INTj - Analyst
ENTj - Director
Interestingly, what you'll notice is that a basic researcher type is missing: The "theorist". Theorists can be INTj-Ne types or ENTp-Ti types, but there is no clear type for this researcher theme. In the MBTI, the theorist theme is best captured by the INTP type. The MBTI, on the other hand, doesn't seem to have an equivalent to the Socionics INTp type.
What this means is that to create a complete personality system, what has to be done is that each basic theme that people can take on has to be captured as a distinct type. The best way to capture the basic themes is to look at the types in each major personality system and analyze what the themes are. Then, once you have an inclusive list, try to think of other themes that are not captured, perhaps by looking at an exhaustive list of famous people, and trying to determine what their basic themes are. This would create a much more complete personality system.