  This study investigates the prospect of discovering strongly interacting
gluinos in different multi-lepton channels with lepton multiplicity greater
than or equal to 2 at LHC RUN-III, considering several pMSSM scenarios. The
effectiveness of the Multivariate Analysis (MVA) method with the Boosted
Decision Tree (BDT) algorithm is explored in order to obtain a better
significance for different models. Promising results are obtained for the
3-lepton channels, indicating that the use of MVA methods can improve the
sensitivity of the search for gluinos at LHC RUN-III. The study probes the
multi-lepton signatures arising from gluinos via intermediate eweakinos and
sleptons at an early stage of the LHC RUN-III. The heavier eweakinos can give
rise to three or four lepton signals in which the squark hierarchy between L
and R types plays a crucial role. The study considers two sets of benchmark
points that satisfy all the collider constraints obtained from the LHC RUN-II
data. Moreover, these sets of benchmark points are mostly consistent with
WMAP/PLANCK data and the muon (g-2) constraint. The corresponding results from
the MVA technique demonstrate that even for an integrated luminosity of 270
$fb^{-1}$, the 5 $\sigma$ discovery prospect of $3l+ jets + \cancel{E_T}$ for
$M_{\widetilde{g}}=1.8$ TeV in the wino type model is promising. The study also
presents the other various models that may show up at the early stage of LHC
RUN-III. The wino type models in the scenario where left squarks are light and
right squarks are heavy, exhibit the best prospect of discovering gluinos in
the multi-lepton channels in the LHC RUN-III experiment. This paper's findings
provide crucial insights into the potential discovery of gluinos in
multi-lepton channels.
