The author understands the subjectin general as the cause of oneself and determines the subjectness of an individualas their ability to be both the source and the result of their own activities. In the present work, the author answers the following question: What is the subject of reproduction in an individual? In comparison with an earlier interpretation of subjectness, the scope of revealed causa suiis specified: possibilities of an individual are discerned which are implemented and acquired by them in the process of activity. The Subject is not the one who has achieved but the one who does everything to achieve. Being the Subject means to produce possibilities of achieving. The criterion of subjectness is the correspondence between the opportunities invested in the process, and the opportunities accumulated in the process of achieving. This way subjectness is determined as the art of dealing with own current possibilities, thus ensuring their extensive reproduction. In the meantime it is postulated that the total amount of potential possibilities of an individual is unlimited (the metaphor of an infinite-dimensional cube is taken). Possibilites are appropriated (M. Heidegger) in the process of an individual’s interaction with environment. They not only contribute to achieving of any other purposes, but they themselves form the goals guiding the activity. There are various possibilities, internal and external, obvious and hidden, newly acquired and actualized, opportunities of support and opportunities of desire. The following is accepted: the higher the level of obvious (manifested) possibilities (I can), the stronger the urge to implement them (I want) (thus not only I want causes I can, but I can challenges I want). The dynamic unity of I can and I want forms the essence of what the author determines as Possibleness of an individual; we mean the possibilities that an individual does not only have but experiences them as existing in him. Possibleness is an experienced feasibility of possibilities. There are conditions of the Possibleness optimum that are based on the mathematical model of Possibleness combining ideas of the variety of possibilities. In this context, subjectness is defined as the Possibleness that meets the optimum criteria (“Get your investments repaid”, “Be efficient”, “Save up”, “Do not skimp on efforts”). An obvious consequence of accepting the Possibleness model is the transition to multi-subject models of personality: they allow to realize the Possibleness optimum conditions in those cases when the one-to-one with the world interaction impedes revealing of subjectness (limited resources of the environment, lack or surplus of desires). There are several models of subject assemblies: self-employed farmer, author — expert, leader — partners, and master — worker. There are some numerical examples given illustrating the effect of achieving the Possibleness optimum in various forms of subject assemblies. In accordance with the law of development of higher mental functions (according to L. Vygotsky) a hypothetical attempt is made to describe the structure of an individual’s personality as a result of interiorization of various subject assemblies. From this point of view we have considered some manifestations of an individual’s self-regulation (taking such forms as volitional, semantic, target-oriented, and operational) when solving a problem to one’s taste. The empirical research shows that in the process of solving such problems each of the inner subjects included in the personality (Autocratic I, With One Other, I Myself, and Capable I) reaches a compliance of the individual’s ambitions and the acquired possibilities. Three variants of the subject organization of personality are described: mono-personality, binary personality,and ternary personality. Both hypothetical and real-life examples of functioning of the individual’s Possibleness model are drawn for different variants of the subject organization of personality. The models presented are the model of an ideal negotiator (Trust, but verify! — How much?), the model of hope and disappointment in love, the model of the triumvirate of subjects, the reinterpreting model of risk-taking by J. Atkinson. The culture presented to an individual in the form of symbolic interactions between different Is (as society in one’s head), is interpreted as a condition for achieving the Possibleness optimum which implies a different level of subject complexity for every personality construction (binary, ternary, tetrary etc.).