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Precise measurements of Higgs boson production in weak-boson fusion at the HL-LHC necessitates revisiting many theoretical studies of this process. I present first steps in this direction, with a focus on contributions from non-factorizable corrections. For the first time, we have combined two-loop virtual corrections, known within the eikonal approximation, with non-factorizable real-virtual and double-real QCD corrections. This makes it possible to study their impact on the various observables in weak-boson fusion.