  We compute the three-loop correction to the universal single-soft emission
current for the case of scattering amplitudes with two additional color-charged
partons. We present results valid for QCD and $\mathcal{N}=4$ super-symmetric
Yang-Mills theory. To achieve our results we develop a new integrand expansion
technique for scattering amplitudes in the presence of soft emissions.
Furthermore, we obtain contributions from single final-state parton matrix
elements to the Higgs boson and Drell-Yan production cross section at
next-to-next-to-next-to-next-to leading order (N$^4$LO) in perturbative QCD in
the threshold limit.
