Models with extended Higgs sectors can contain several additional Higgs states, heavier or lighter than the SM Higgs boson. The couplings of lighter extra states to SM particles can be strongly reduced, leading to small cross sections for their direct production. Heavier extra states can have larger couplings to SM particles and, moreover, have large branching fractions into lighter extra states, notably into a SM-like Higgs boson accompagnied by another Higgs state which can be lighter or heavier than 125$sim$GeV. Motivated by corresponding scenarios in the NMSSM we study the prospects for the discovery or exclusion of cascade decays $ggF to H_3 to H_2 + H_1$ in the $bbar{b}bbar{b}$, $bbar{b}tautau$ and $bbar{b}gammagamma$ final states where either $H_1$ or $H_2$ can be SM-like. Significant regions of the NMSSM parameter space can be tested by these searches. These are, however, not confined to models of the NMSSM type.
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