  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
$b\bar{b}b\bar{b}$, $b\bar{b}\tau\tau$ and $b\bar{b}\gamma\gamma$ 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.
