In this proceeding we report on
the recent study [1] performed in the context of
nested soft-collinear subtraction [2].
The scheme is designed to provide a
fully differential and analytic subtraction method for
infrared singularities at next-to-next-to-leading order (NNLO) in QCD.
At variant with respect to the first formulation
of the nested soft-collinear subtraction,
Ref. [1] aims at organising the
subtraction procedure in a way that allows
for a drastic reduction of the complexity related
to the proliferation of the subtraction terms, and
at dealing with arbitrary final states.
In this document we highlight a crucial aspect
of the analysis of Ref. [1]:
the idea of rearranging NNLO subtraction terms
as iterations of few universal structures identified at NLO.