This article proposes extending the empirical sociological debate regarding the complex ways social classifications construct scenarios of subjectivity. Based on the case study of the Boarding School for the Gifted Disadvantaged in Israel, the article describes how a new cultural order created a new scenario of subjectivity (“gifted disadvantaged”) that had not been known before. This scenario was shaped in relation both to the ethnic classification in Israel, as well as to two social categories that were well-known in the educational field (“gifted” and “disadvantaged”). To understand the institutional dynamics involved in the construction of a new scenario of subjectivity, content analysis of the organizational documents that accompanied the founding of the school was carried out, and in-depth interviews with graduates of the school were conducted in order to understand how those who populate the new scenario experience their subjectivity years after its construction. The findings indicate a specific connection between classifications, subjectivity, and personal visibility. Specifically, the study reveals a number of phenomenological aspects that enhance the experience of visibility: the cognitive identification of two types of self; the experience of cognitive liminality; and the consciousness of having a subjectivity deserving of special nurturance.