  The Next-to-Minimal Supersymmetric Standard Model (NMSSM), the singlet
extension of the MSSM which fixes many of the MSSM's shortcomings, is shown to
be within reach of the upcoming runs of the Large Hadron Collider (LHC). A
systematic treatment of the various Higgs decay channels and their interplay
has been lacking due to the seemingly large number of free parameters in the
NMSSM's Higgs sector. We demonstrate that due to the SM-like nature of the
observed Higgs boson, the NMSSM's Higgs and neutralino sectors have highly
correlated masses and couplings and can effectively be described by four
physically intuitive parameters: the physical masses of the two CP-odd states
and their mixing angle, and $\tan\beta$, which plays a minor role. The heavy
Higgs bosons in the NMSSM have large branching ratios into pairs of lighter
Higgs bosons or a light Higgs and a $Z$ boson. Search channels arising via
these Higgs cascades are unique to models like the NMSSM with a Higgs sector
larger than that of the MSSM. In order to cover as much of the NMSSM parameter
space as possible, one must combine conventional search strategies employing
decays of the additional Higgs bosons into pairs of SM particles with Higgs
cascade channels. We demonstrate that such a combination would allow a
significant fraction of the viable NMSSM parameter space containing additional
Higgs bosons with masses below 1 TeV to be probed at future runs of the LHC.
