Background: Rooted in problems of social justice, intersectionality addresses intragroup differences in impacts and outcomes and the compound discrimination at specific intersections of classification (Crenshaw,1991). It stresses that deficits/debts in outcomes often occur non-additively; for example, discriminatory hiring practices can be especially pronounced for Black females, with total deficits/debts for the group being more than the sum of deficits for females on average, plus deficits for Black individuals on average (Crenshaw,1991). Intersectionality has both normative theoretical and empirical research dimensions (Hancock,2007). Over the past 15 years several quantitative approaches to intersectionality have been developed (e.g., Bauer,2014; Whitebread et al.,2023). Objective: The objective is to describe three main analytic considerations and four challenges/caveats to support critical use of methods of quantitative intersectionality. Both hypothetical and empirical examples are used. Program: The empirical example consists of a cluster randomized trial evaluating the impact of an inquiry-based science, math and technology program for students in grades 4-8. Research Design: The single empirical example draws on an 82-school randomized trial conducted in the southern United States. Results: We offer three considerations, framed as questions, for addressing problems of intersectionality: Consideration 1:Is the aim to understand heterogeneity of outcomes between one factor across levels of another factor? Analysis of interactions effects across groups is central to quantitative intersectionality (McMaster et al.,2019). It allows analysis of compound (multiplicative) effects. However, without deeper contextualization, an unguided study of interaction effects can be problematic (e.g., categories should be justified [Blissett et el.,XXXX]; modeling assumptions should be tested [Whitebread et al.,2023].) Consideration 2:Is the aim to understand heterogeneity of outcomes relative to a socially desirable criterion? The quantitative study of intersectionality is not reducible to just the study of interactions. Regression models with just main effects can demonstrate variation in predicted values for different groups with no interaction effects. If group outcomes are rated against performance criteria (e.g., admission to prestigious colleges), specific groups may be disproportionately negatively affected. Consideration 3:Do unique to group variable play a role? An aspect of intersectionality seldom discussed (and the main idea of this work) is the role of "unique to group" variables that restrict certain points of intersection for a given sample. A hypothetical example is the experience of "hafu" students (mixed race, with one Japanese parent and one non-Japanese parent) in Japan. Such students experience discrimination in school settings (Oshima,2014; Taba,2021; Taguchi,2016). If the study sample consists of all student in grades 6-8 in public schools in Japan, one may examine outcomes at specific intersections of three factors: "whether one is mixed-race" x "whether one has a mixed-race mentor" x "whether one experiences anti-mixed-race discrimination at school" A compelling hypothesis concerning achievement outcomes across the intersections of these three factors is that having a mixed-race mentor offsets/moderates the effects of discrimination experienced by mixed-race students as it affects achievement. Importantly this example demonstrates a problem of intersectionality that cannot be covered by the first two considerations. Specifically, for the assumed sample, non-hafu children, by definition, cannot experience either the discrimination or the potential offsetting effect of having a mixed-race mentor. This has implications for framing the problem in quantitative terms A second empirical example further highlights intersectionality that requires the third consideration. Exploratory findings from a cluster randomized trial (Author,XXXX) that evaluated the impact of a reform-based math, science and technology program included: less positive impact for minority students by -2.72 scale score units(SSU) (p<0.01) compared to non-minorities, and less positive impact of 1.50 SSU for each quartile increase in proportion minority students at the school level (p<0.01) . These moderated effects persisted even after controlling for possible confounding on moderators including in levels of SES, pretest, gender, ELL-status and grade level. An intersectional approach to analysis that focuses on interactions would seek to understand the alternative mechanisms of school conditions that produce debts/disparities in outcomes at the person- and school-levels. This is consistent with Consideration 1; however, this would miss an important detail: In eight of the schools all of the students were minorities. Such schools would present a gap in intersections between student-groups and school-groups. Simply put: only minority students can belong to all-minority schools, which means that the analysis of outcomes for certain intersections of categories, and corresponding explanations, apply to only certain groups. This may be easily missed using models that cross (School proportion minority)x(minority status of student). The distinction may also seem trivial if quantitative models are expected to "iron out" the more-outlying school cases. The framework of intersectionality would prioritize a mixed-methods evaluation of program implementation and experience in the eight all-minority schools that represent a unique combination of circumstances. The four challenges/caveats with intersectional analysis are. (1) The potential for thinning out of the sample from examining too many points of intersection (with implications for statistical power), (2) The potential for mutually exclusive sets of factors providing complementary accounts of heterogeneity of outcomes across intersections. And two standard caveats for use with regression analysis that may affect the validity of inferences from quantitative analysis of intersectionality (3) The potential for results to depend on non-linearity in variables, or non-linearity of regression parameters (Bauer et al., 2021). (4) Interaction effects specify differences in "change in y-on-x slopes" but not the fixed location of slopes relative to x-y axes necessary for interpretation. Conclusions: Methods of quantitative intersectionality continue to be debated and developed. The normative aspects emphasize the rootedness of methods in substantive issues regarding power relations and social justice. The normative considerations keep us mindful of the substance of what is being studied -- the categories considered, the partners involved in defining research questions, and the mixed methods that must be employed to better understand the role of certain variables, including the "unique to persons" variables, such as the role of pairing hafu students with hafu mentors, or the experiences of minority students in all-minority schools. Important subgroups, with "unique to persons" attributes, may be too easily lost in overarching models heavily saturated with effects.