We consider what multiple Higgs interactions may yet reveal about the scalar sector. We estimate the sensitivity of a Feynman topology-templated analysis of weak boson fusion Higgs pair production at present and future colliders — where the signal is a function of the Higgs coupling modifiers κ V , κ 2V , and κ λ . While measurements are statistically limited at the LHC, they are under general perturbative control at present and future colliders, departures from the SM expectation give rise to a significant future potential for BSM discrimination in κ 2V . We explore the landscape of BSM models in the space of deviations in κ V , κ 2V , and κ λ , highlighting models that have measurable order-of-magnitude enhancements in either κ 2V or κ λ , relative to their deviation in the single Higgs coupling κ V .