  We describe how the nested soft-collinear subtraction scheme [1] can be used
to compute the next-to-next-to-leading order (NNLO) QCD corrections to the
production of an arbitrary number of gluonic jets in hadron collisions. We show
that the infrared subtraction terms can be combined into recurring structures
that in many cases are simple iterations of those terms known from
next-to-leading order. The way that these recurring structures are identified
and computed is fairly general, and can be applied to any partonic process. As
an example, we explicitly demonstrate the cancellation of all singularities in
the fully-differential cross section for the $q\bar{q} \to X + N g $ process at
NNLO in QCD. The finite remainder of the NNLO QCD contribution, which arises
upon cancellation of all $\epsilon$-poles, is expressed via relatively simple
formulas, which can be implemented in a numerical code in a straightforward
way. Our approach can be extended to describe arbitrary processes at NNLO in
QCD; the largest remaining challenge at this point is the combinatorics of
quark and gluon collinear limits.
