  We combine NLO predictions with full top-quark mass dependence with
approximate NNLO predictions for Higgs-boson pair production in gluon fusion,
including the possibility to vary coupling parameters within a non-linear
Effective Field Theory framework containing five anomalous couplings for this
process. We study the impact of the anomalous couplings on various observables,
and present Higgs-pair invariant-mass distributions at seven benchmark points
characterising different $m_{hh}$ shape types. We also provide numerical
coefficients for the approximate NNLO cross section as a function of the
anomalous couplings at $\sqrt{s}=14$ TeV.
