Scattering amplitudes are expected to admit a factorised structure in special kinematic limits, such as the Regge, soft and collinear limits. However, less is known about the precise mechanisms through which factorisation of n-particle scattering amplitudes is realised at high perturbative orders, where more complex structures arise. Starting with the soft anomalous dimension, in this talk I will discuss the multi-particle collinear limits of massless amplitudes at three- and four-loop orders. In particular, I will demonstrate how strict collinear factorisation of multiple massless final-state coloured particles is achieved, and show that the conditions on the structure of the soft anomalous dimension required by two-particle collinear limits are sufficient to guarantee factorisation also in any multiple collinear limit. I will also discuss new constraints on the soft anomalous dimension that arise from multi-collinear limits for amplitudes containing massive coloured particles.