  If no new physics signals are found, in the coming years, at the Large Hadron
Collider Run-2, an increase in precision of the Higgs couplings measurements
will shift the dicussion to the effects of higher order corrections. In Beyond
the Standard Model (BSM) theories this may become the only tool to probe new
physics. Extensions of the Standard Model (SM) with several scalar singlets may
address several of its problems, namely to explain dark matter, the
matter-antimatter asymmetry, or to improve the stability of the SM up to the
Planck scale. In this work we propose a general framework to calculate one
loop-corrections in BSM models with an arbitrary number of scalar singlets. We
then apply our method to a real and to a complex scalar singlet models. We
assess the importance of the one-loop radiative corrections first by computing
them for a tree level mixing sum constraint, and then for the main Higgs
production process $gg \to H$. We conclude that, for the currently allowed
parameter space of these models, the corrections can be at most a few percent.
Notably, a non-zero correction can survive when dark matter is present, in the
SM-like limit of the Higgs couplings to other SM particles.
