Triple Higgs boson production at a 100 TeV proton-proton collider

We consider triple Higgs boson production at a future 100 TeV proton-proton collider. We perform a survey of viable final states and compare and contrast triple production to Higgs boson pair production. Focussing on the $hhh \rightarrow (b\bar{b}) (b\bar{b}) (\gamma \gamma)$ final state, we construct a baseline analysis for the Standard Model scenario and simple deformations, demonstrating that the process merits investigation in the high-luminosity phase of the future collider as a new probe of the self-coupling sector of the Higgs boson.