This secondary analysis of data from a randomized control trial of an early mathematics intervention, ROOTS, explored whether patterns of intervention response were best categorized by the typical response/non-response binary or a more complex framework with additional response profiles. Participants included kindergarten students at risk for mathematics difficulties who were randomly assigned to the ROOTS intervention condition (n = 880). Results of a latent profile analysis indicated that variability in response to the ROOTS intervention was best captured by a more complex categorization framework encompassing four distinct response profiles: a moderate-risk, initial mild response group; a moderate-risk, delayed response group, a high-risk, strongly responsive group; and a lower-risk, non-responsive group. Membership in each response profile was predicted by pre-intervention performance on measures of both mathematics and cognitive skills (visual-spatial, fluid reasoning, and working memory). On average, students with lower initial mathematics skill and cognitive performance demonstrated stronger intervention response. Findings suggest that more complex frameworks may capture important variability in responsiveness to evidence-based early mathematics intervention, with implications for next steps to adequately support distinct subgroups of students with mathematics difficulties. [This paper will be published in "Journal of Research on Educational Effectiveness."]