The goal of this project is to advance theoretical predictions for a number of relevant benchmark processes for Higgs boson production at the LHC that combine higher-order QCD corrections and effects of higher-dimensional operators. For Higgs production in weak boson fusion and Higgs associated production we aim at a combination of NNLO QCD corrections and anomalous couplings. For Higgs pair production, NLO electroweak corrections will be included, for Higgs production in association with two jets the NLO QCD corrections with full top quark mass dependence will be calculated.