Learners' active participation and involvement in English classes and tasks is called "learner engagement" and has been the focus of much attention in recent second language acquisition (SLA) research. Engagement is characterized by the fact that it attempts to capture the learner's motivated state from multiple perspectives, including behavioral, cognitive, emotional, social, and agentic dimensions. On the other hand, most engagement research to date has focused on one of the above aspects, and it is not clear how each aspect relates to each other and influences actual learning outcomes. Against this backdrop, our study aimed to determine what kind of relationship (i.e., combination) is found in each aspect of engagement, and how this combination is related to learners' ideal L2 self and English proficiency. Participants of the study were 360 Japanese junior high school English-as-a-foreign-language (EFL) students. A questionnaire-based survey was administered, and the obtained data were analyzed using cluster analysis and one-way analysis of variance (ANOVA). The results showed that the participating students fell into three groups with different engagement profiles. Furthermore, the group with high means for all of the dimensions of engagement had the clearest ideal L2 self and the highest proficiency compared to the other two groups. Based on the results, we argue that language teachers may be able to work on one dimension of learner engagement (e.g., emotional dimension) to positively influence the other dimensions (e.g., behavioral/cognitive dimensions) and thus consequently promote the desired learning outcomes.