  Physics beyond the Standard Model (SM) may manifest itself as small
deviations from the SM predictions for Higgs signal strengths at 125 GeV. Then,
a plausible and interesting possibility is that the Higgs sector is extended
and at the weak scale there appears an additional Higgs boson weakly coupled to
the SM sector. Combined with the LEP excess in $e^+e^-\to Z(h\to b\bar b)$, the
diphoton excess around 96 GeV recently reported by CMS may suggest such a
possibility. We examine if those LEP and CMS excesses can be explained
simultaneously by a singlet-like Higgs boson in the general next-to-minimal
supersymmetric Standard Model (NMSSM). Higgs mixing in the NMSSM relies on the
singlet coupling to the MSSM Higgs doublets and the higgsino mass parameter,
and thus is subject to the constraints on these supersymmetric parameters. We
find that the NMSSM can account for both the LEP and CMS excesses at 96 GeV
while accommodating the observed 125 GeV SM-like Higgs boson. Interestingly,
the required mixing angles constrain the heavy doublet Higgs boson to be
heavier than about 500 GeV. We also show that the viable region of mixing
parameter space is considerably modified if the higgsino mass parameter is
around the weak scale, mainly because of the Higgs coupling to photons induced
by the charged higgsinos.
