  We investigate multi-Higgs boson production at proton colliders, in a
framework involving anomalous interactions, focusing on triple Higgs boson
production. We consider modifications to the Higgs boson self-couplings, to the
Yukawa interactions, as well as new contact interactions of Higgs bosons with
either quarks or gluons. To this end, we have developed a MadGraph5_aMC@NLO
loop model, publicly available at
https://gitlab.com/apapaefs/multihiggs_loop_sm, designed to incorporate the
relevant operators in the production of multiple Higgs bosons (and beyond). We
have performed cross section fits at various energies over the anomalous
interactions, and have derived constraints on the most relevant anomalous
coefficients, through detailed phenomenological analyses at proton-proton
collision energies of 13.6 TeV and 100 TeV, through the 6 $b$-jet final state.
