  The $U(1)_{L_\mu-L_\tau}$ extended Standard Model (SM) is anomaly free, and
contains a massive $Z^\prime$ boson. The associated Higgs, which generates the
$Z'$'s mass via spontaneous symmetry breaking (SSB) can mix with the SM Higgs.
The new parameters relating to extra Higgs cannot be probed at the LHC with
final states containing no more than $4$ leptons. Therefore, we use signatures
with at least $6$ leptons to probe the parameter space through LHC experiments.
Since SM predicts a lower cross section for a final state with at least $6$
leptons than is currently visible at the LHC, the background is negligible,
thereby making this channel an extremely sensitive probe. We find that in a
limited region of the parameter space this channel can strongly constrain the
associated $U(1)_{L_\mu-L_\tau}$ coupling constant, even more so than for a $4$
lepton or fewer final state.
