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. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd