Coming from a previous-generation collider experiment, CDF, with a lower energy and luminosity reach, I was intrigued by the potential of CMS for new physics searches using the Run-II dataset, collected during 2016-2018, of nearly two times the energy and five times the luminosity of the Run-I sample from 2009-2012. I joined the Innovative Training Network (ITN) “Advanced Multivariate Analyses for New Physics Searches” (AMVA4NewPhysics) as the PI of the Institute of Accelerating Systems and Applications (IASA), one of the nodes of the ITN. The network, as its name states, was focused on the development of advanced machine learning (ML) algorithms for searches for physics beyond the standard model (BSM) with participation of scientists from both ATLAS and CMS. My interest in new physics was mostly driven by the theory of Supersymmetry (SUSY) as the most popular and exhaustively studied theory among all BSM theories. SUSY provides plausible answers to questions unanswered in the context of the standard model (SM), such as the naturalness of the Higgs boson mass and the nature of the dark matter. I was involved in a research program that was extended beyond the AMVA4NewPhysics lifetime (2015-2019) and produced three PhD theses and the corresponding number of peer-reviewed CMS publications. This program targeted a variety of signatures, with the results interpreted in the context of simplified R-parity conserving SUSY models; for example, the production of electroweakinos with nearly degenerate mass decaying to soft leptons and missing transverse momentum or gluinos decaying to a single lepton, missing transverse momentum and a large number of jets. In the first analysis, the small mass difference between SUSY particle states, referred to as the “compressed mass spectrum” scenario, leads to very soft final-state leptons requiring low-threshold triggers for their detection, while they are also challenging to reconstruct. In the second analysis, the large hadronic activity in the final states requires development of sophisticated techniques for the discrimination of signal and background, which is copiously produced via SM processes. These searches used the full sample of Run-II CMS data and provided important contributions to the LHC new physics search program by extending significantly the excluded regions of the parameter space of SUSY simplified models.