Abstract Broadbent and Calcott's breakage matrix methodology has been used for more than 50 years to model various comminution processes and to determine breakage functions from experimental data. The methodology assumes first-order law of breakage and neglects mechanical multi-particle interactions that are especially prevalent in dense-phase comminution processes and breakage tests. Although several researchers severely criticized this aspect of the methodology, Baxter et al. (2004, Powder Technol. 143–144:174–178) were the first to modify the methodology toward determining the elements of a feed-dependent breakage matrix. However, no non-linear breakage matrix has ever been constructed from experimental data using the modified approach. In this study, a critical analysis of this modified approach has been performed, and the non-linear breakage matrix was fundamentally derived from a non-linear population balance model. Different approaches were proposed to identify the breakage functions based on the nature of available breakage tests on multiple mono-dispersed feed samples and at least one poly-dispersed sample. Using the derived equations, available experimental data on the breakage of a binary mixture of coarse and fine limestone particles in uniaxial compression test were fitted to quantify the multi-particle interactions. Superior fitting capability of rational approximation to the effectiveness factor was demonstrated.