We present a systematic framework for the calculation of soft functions that are defined in terms of N ≥ 2 light-like Wilson lines. The formalism represents an extension of a method that we developed earlier for the calculation of dijet soft functions to the general N-jet case. We discuss the technical aspects of this generalisation, focussing on SCET-1 soft functions that obey the non-Abelian exponentiation theorem in this contribution. As a first application of our method, we consider the N-jettiness observable and present numerical results for the 1-jettiness and 2-jettiness hadron-collider soft functions to next-to-next-to-leading order in the perturbative expansion.
