In this paper, teacher educators located at three different universities across the United States share findings emerging from our collaboration around a suite of three activities that engage our teacher candidates (TCs) around their identities as future mathematics teachers. In particular, our TCs engaged in a suite of identity-based activities in order to promote reflexivity across dimensions in a way that we argue is not possible through a single activity. We implemented activities to promote our TCs' reflexivity, as well as to engage in critical self-reflection on our own practice as mathematics teacher educators. We explore the relationship between multidimensional reflexivity and beginning teachers who hold commitments toward justice and equity in mathematics education. Three activities -- a mathematics autobiography, a silhouette, and an identity card sort -- were selected, modified, implemented, and reflected on across our secondary mathematics methods courses, with the goal of promoting reflexivity across dimensions. We refer to "reflexivity across dimensions" as one's ability to explore one's identity within various analytical frames. The autobiography, silhouette, and card sort offered opportunities for TCs to explore the dimensions of their "narrative," "discursive," and "categorical" reflexivity, respectively. We found that TCs engaged in continual questioning and perturbing of their positions in society in ways that contributed to their sense of self and promoted reflexivity across the dimensions of TCs' mathematics identities.