  We study the prospects of a simultaneous hunt at the Large Hadron Collider
(LHC) of relatively light electroweakinos and a singlet-like scalar of the
$Z_3$-symmetric Next-to-Minimal Supersymmetric Standard Model ($Z_3$-NMSSM) in
the cascade decays of not so heavy ($\lesssim 1.5$ TeV) top squarks that are
produced in pairs at the LHC which characteristically involve the singlet-like
states. We work in a scenario where the lightest (next-to-lightest) SUSY
particle is bino (singlino)-like with a mass below 100 GeV ($\gtrsim 100$ GeV),
whereas a pair of immediately heavier neutralinos and the lighter chargino are
higgsino-like with masses in the range $\sim 500$ GeV -- 1 TeV. Further, the
singlet-like scalar present in the spectrum provides a funnel for a rapid
enough mutual annihilation of the LSP thus making the latter meet the
experimental upper bound on its relic abundance. The scenario is motivated by
its ability to offer a bino-like dark matter with such a mass unlike what is
now disfavored in the MSSM while avoiding the stringent lower bounds from the
LHC experiments on the masses of these involved particles and still remaining
reasonably `natural'. We find that while a usual cut-based analysis (CBA) on
LHC data worth 300 $\text{fb}^{-1}$ would be unable to discover such
excitations, a multivariate analysis (MVA) can be reasonably sensitive to
higgsino-like electroweakinos having masses $\gtrsim 650$ GeV when the lighter
top squark has a mass $\gtrsim 1$ TeV. On the other hand, with 3000
$\text{fb}^{-1}$ of data these masses become accessible in a CBA while even an
MVA on such a data set is unlikely to find these electroweakinos with masses
around 1 TeV when the mass of the lighter top squark hits $\sim 1.5$ TeV.
