  There could be another scalar in nature quasi-degenerate with the observed
one (h125). This is possible in models such as the Next-to-Minimal
Supersymmetric Standard Model (NMSSM). The scenario(s) with a single Higgs
boson can be compared to that with multiple ones, all near 125 GeV. In order to
assess the extent to which the current set of collider, cold dark matter relic
density and direct detection limits are capable of discriminating these
scenarios, we perform, for the first-time, global fits of a weak-scale
phenomenological NMSSM with 26 free parameters using the nested sampling
implementation in PolyChord, a next-generation tool for Bayesian inference. The
analyses indicate that the data used shows a moderate tendency for supporting
the scenario with an additional scalar much lighter than h125 with mass
distribution centred below the W-boson mass.
  More stringent constraints are, however, needed for decisive inference
regarding an additional Higgs boson with mass much less than or near 125 GeV.
