  We consider improving POWHEG+MINLO simulations, so as to also render them NLO
accurate in the description of observables receiving contributions from events
with lower parton multiplicity than present in their underlying NLO
calculation. On a conceptual level we follow the strategy of the so-called
MINLO' programs. Whereas the existing MINLO' framework requires explicit
analytic input from higher order resummation, here we derive an effective
numerical approximation to these ingredients, by imposing unitarity. This
offers a way of extending the MINLO' method to more complex processes,
complementary to the known route which uses explicit computations of
high-accuracy resummation inputs. Specifically, we have focused on
Higgs-plus-two-jet production (HJJ) and related processes. We also consider how
one can cover three units of multiplicity at NLO accuracy, i.e. we consider how
the HJJ-MINLO simulation may yield NLO accuracy for inclusive H, HJ, and HJJ
quantities. We perform a feasibility study assessing the potential of these
ideas.
