Internships are increasingly promoted as a high impact practice to improve students' post-graduation employment outcomes, and educators often encourage students to participate in multiple internships. Yet, there is a lack of research on the sociocultural contexts associated with multiple internship participation. We present findings about the culture of multiple internship participation -- drawing on focus groups and one-year follow-up interviews with students at five colleges in the United States, along with interviews with their educators and an analysis of online documents about multiple internship participation. The evidence documents a particular culture of the multiple internship economy, representing multiple internships as a linear, progressive, goal-oriented cultural project to accumulate a marketable self; also described by anthropologists as a neoliberal conception of the self. This cultural conception of a marketable neoliberal self is comprised of signs -- such as narratives of multiple internships -- that provide evidence of skills and experiences, of persevering through obstacles, and of 'hustle' and a 'do what it takes' attitude, which can be deployed to navigate competitive gatekeeping encounters such as employment interviews. Based on these findings, we develop a sociocultural theory of multiple internship participation as a project of neoliberal gatekeeping navigation.