  We extend our algorithm for automating the calculation of two-loop dijet soft
functions to observables that do not obey the non-Abelian exponentiation
theorem, i.e. to those that require an independent calculation of the
uncorrelated-emission contribution. As the singularity structure of
uncorrelated double emissions differs substantially from the one for correlated
emissions, we introduce a novel phase-space parametrisation that isolates the
corresponding divergences. The resulting integrals are implemented in SoftSERVE
1.0, which we release alongside of this work, and which we supplement by a
regulator that is consistent with the rapidity renormalisation group framework.
Using our automated setup, we confirm existing results for various jet-veto
observables and provide a novel prediction for the soft-drop jet-grooming
algorithm.
