After a brief introduction to the problem of subtraction of infrared divergences for high-order collider observables, we present a preliminary study of strongly-ordered soft and collinear multiple radiation from the point of view of factorisation. We show that the matrix elements of fields and Wilson lines that describe soft and collinear radiation in factorised scattering amplitudes can be re-factorised in strongly-ordered limits, providing a systematic method to compute them, to characterise their singularity structure, and to build local subtraction counterterms for strongly-ordered configurations. Our results provide tools for a detailed organisation of subtraction algorithms, in principle to all orders in perturbation theory.