  We consider QCD radiative corrections to the production of colourless
high-mass systems in hadron collisions. We show that the recent computation of
the soft-virtual corrections to Higgs boson production at N$^3$LO [1] 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 N$^3$LL 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 N$^3$LO corrections for the production of an arbitrary colourless
system. In the case of the Drell-Yan process, we confirm the recent result of
Ref.[2].
