Yes, there are other ersonality classifications rather than big five. I am thinking of Hans Eysenck' work. I am attaching to this post a Word file Eiysenck's calssification of types of personalities. I got the material from Internet. As far as I know Eysenck's classification appeared firts than the Big Five of personality.
While the bias of researchers currently shows only a few articles on the C. G. Jung personalilty types and the derived Myers-Briggs Type Indicator, I suggest that there is a strong overlap between the MBTI 'temperaments' (type clusters) and the NEO-5: MBTI Sensate Thinkers = NEO-5 Conscientiousness; Sensate Feelers = Agreeableness; Intuitive Thinkers = Openness; and -- which demonstrates the robust bias of NEO-5; Intuitive Feelers = Neuroticism (a NEO-5 category taken from Eysenck). Why the NEO-5 bias? Because the researchers who designed it appear to be, in the MBTI terms, Intuitive Thinkers and Sensate Thinkers. The NEO-5 is psychologically damaging when used to give results to Intuitive Feelers, including people of who have spiritual, body empathic and other creative traits, since it tends to label them 'neurotic'. Personality theorists have tried to remedy this failure of the NEO-5, for example, see the notion of "highly sensitive persons".