  Motivated by a $\sim 3\sigma$ excess recorded by the CMS experiment at the
LHC around a mass of order $\sim 137$ GeV in $ZZ\to 4l$ and $\gamma\gamma$
samples, we analyse the discovery potential of a second neutral Higgs boson in
the Supersymmetric $B-L$ extension of the Standard Model (BLSSM) at the CERN
machine. We confirm that a double Higgs peak structure can be generated in this
framework, with CP-even Higgs boson masses at $\sim125$ GeV and $\sim137$ GeV,
unlike the case of the Minimal Supersymmetric Standard Model (MSSM).
