We consider QCD radiative corrections to the production of colorless high-mass systems in hadron collisions. We show that the recent computation of the soft-virtual corrections to Higgs boson production at N3LO  together with the universality structure of soft-gluon emission can be exploited to extract the general expression of the hard-virtual coefficient that contributes to threshold resummation at N3LL accuracy. The hard-virtual coefficient is directly related to the process-dependent virtual amplitude through a universal (process-independent) factorization formula that we explicitly evaluate up to three-loop order. As an application, we present the explicit expression of the soft-virtual N3LO corrections for the production of an arbitrary colorless system. In the case of the Drell-Yan process, we confirm the recent result of Ref. .