  The possibility of identification of an observable CMS $\mu^+ \mu^-$ excess
at 28 GeV in the channel $pp\to \mu^+ \mu^- b \bar b$ at $\sqrt{s}$=8 TeV and
13 TeV as a manifestation of one of the minimal supersymmetric standard model
(MSSM) Higgs bosons is investigated. The MSSM parametric scenarios in the
regime of large threshold corrections involving low-mass CP-odd scalar, a 125
GeV CP-even scalar and other Higgs bosons with suitable masses are found, where
the alignment limit conditions for the Higgs couplings are respected.
Perturbative unitarity bounds and constraints on the electroweak vacuum
stability are discussed in the regime of substantial couplings with the top-
and bottom superpartners. LHC phenomenology including top-quark decay in such a
regime is analyzed.
