Flipped classroom (FC) courses, where students complete pre-class activities before attending interactive face-to-face sessions, are becoming increasingly popular. However, many students lack the skills, resources, or motivation to effectively engage in pre-class activities. Profiling students based on their pre-class behavior is therefore fundamental for teaching staff to make better-informed decisions on the course design and provide personalized feedback. Existing student profiling techniques have mainly focused on one specific aspect of learning behavior and have limited their analysis to one FC course. In this paper, we propose a multi-step clustering approach to model student profiles based on pre-class behavior in FC in a multi-dimensional manner, focusing on student effort, consistency, regularity, proactivity, control, and assessment. We first cluster students separately for each behavioral dimension. Then, we perform another level of clustering to obtain multi-dimensional profiles. Experiments on three different FC courses show that our approach can identify educationally-relevant profiles regardless of the course topic and structure. Moreover, we observe significant academic performance differences between the profiles.