The present study represents a novel method not yet used in the quantitative intersectionality literature -- the CT-C(M-1) model (Eid et al., 2003) -- for measuring and understanding the similarities and uniquenesses among intersectional subgroups. Intersectionality is a conceptual framework from which to investigate and remedy the ways in which oppression manifests at the intersections of socio-politico-geo-temporal power structure contexts and individuals' interwoven experiences of racism, sexism, and other forms of marginalization (Cho et al., 2013). Specifically, we describe and illustrate the usefulness of the CT-C(M-1) model in intersectionality research through estimation of the latent variable structure of two school climate variables (engagement and support) using data from N = 165 schools in which Black non-Hispanic students' experience is centered as the reference category, and which other race-ethnicity subgroups are compared. Consistent with prior research, our substantive findings indicated that, while a large share of commonality among subgroups was observed, Black Hispanic students experienced school climate differently from the other groups. This analytic tool adds to the growing set of quantitative methods that can aid in advancing the second goal of intersectionality research -- intervening in the status quo for true transformational change.