Infrared subtraction algorithms beyond next-to-leading order necessitate the analysis of multiple infrared limits of scattering amplitudes, where several particles sequentially become soft or collinear. In this contribution, we report on the study performed in arXiv:2403.11975, which investigates these limits from the perspective of infrared factorisation, offering general definitions for strongly-ordered soft and collinear kernels, expressed in terms of gauge-invariant operator matrix elements. These definitions facilitate the identification of local subtraction counterterms for strongly-ordered configurations, whose integrals are designed to cancel the IR poles of real-virtual counterterms. This framework is validated at tree level for multiple emissions, and at one loop for single and double emissions.

10 pages. Contribution to the Proceedings of the Loops and Legs in Quantum Field Theory conference (LL2024)