We discuss a path [1] toward the generalisation of the nested soft-collinear subtraction scheme [2] to arbitrary 2 → n processes. The scheme is designed to provide an efficient and process- independent procedure to extract and regulate infrared (IR) singularities arising from unresolved real radiation and combine them with explicit singularities in virtual corrections. The new approach is based on a reorganisation of the relevant subtraction terms into simple combinations of a relatively small number of recurring structures. This strategy leads to a drastic reduction in the computational effort required to derive integrated subtraction terms, while preserving the full generality of the scheme. We believe that this approach will allow for tackling the issue of regularising IR divergences at next-to-next-to-leading order in the strong coupling constant for arbitrary, multi-parton processes.