Back in 2002 I was learning about the Myers-Briggs Type Indicator. I asked psychotherapist Dee Ann whether there were any attributes of personality which were not captured by it. She replied that pathologies (such as schizophrenia) were outside the scope. But in fact the limitations of personality classification schemes arise in quite ordinary circumstances.
Compare person A who is widely seen as a "force of nature" with person B who is polite, civilized and restrained to a fault. In Freudian terms we can say the first person has an ego strongly dominated by the id with relatively weak superego control. For person B it's the reverse. Interestingly, A thinks B is inauthentic and over-compliant; B thinks A is impulsive and under-controlled.
In more modern language, we talk about subconscious drives emanating from the limbic regions of the brain and cortical regulatory inhibition.
The Myers-Briggs Type Indicator does say something about the interaction between subconscious/id, ego and superego; it's framed as the contrast between the persona and the shadow. The paradigm is not, however, that of Myers-Briggs type distinction per se but the breakdown of the normal typological presentation of self mediated by fatigue, stress and the like.
Note: Adrian Raine's book 'The Anatomy of Violence' is extremely informative about the connection between brain functioning and behaviour (and not just criminal behaviour).