We provide a conceptual analysis of how combinatorics problems have the potential to support students to establish non-linear meanings of multiplication (NLMM). The problems we analyze we have used in a series of studies with 6th, 8th, and 10th grade students. We situate the analysis in prior work on students' quantitative and multiplicative reasoning, specifically identifying how combinatorics problems have the potential to support students to establish relationships among one, two, and three-dimensional quantities. As part of the analysis, we identify why there is a need for novel approaches to NLMM.