"Adequate" modifies "Theory", not "Personality" ... :-)
Consider three kinds of personality theory.
1. The standard 'Big 5' 'traits' model with the mnemonic of OCEAN (Openness to experience, Conscientiousness, Extraversion, Agreeableness, Neuroticism/emotional stability).
2. The Keirsey theory of four temperaments - [Guardian, Artisan, Idealist, Rational].
3. Jungian typological theory, in its Myers-Briggs form of 16 types.
It seems to me that there are three interesting issues.
a. To what extent are all three approaches really addressing the same underlying reality (so that a formal correspondence can be established between them)? For example, correlations are shown between the 'Big 5' traits and the four MBTI dimensions - see the bottom of the page ('Statistical Studies') here.
b. What kind of brain architecture would generate the observed diversity of personality/ temperament across individuals? For example, is there a superego-like module which encodes social norms and which inhibits 'selfish' impulses from the lower brain regions? If so, would variations in the 'strength' of this module explain Guardian-Artisan differences (SJ vs. SP) --- or conscientiousness, if you like?
c. What is the evolutionary psychology framework for understanding the evolution of personality differences? It seems likely that there is some merit in having some people who care about social norms, others who are more motivated by risk and excitement, others who can inspire and empathise, and finally people who can think a bit (aka 'intellectuals'). Can formal evolutionary models and simulations make this intuition something testable?
It's not obvious there is much research today on these topics, more's the pity.