Abstract: Supersymmetry (SUSY) is one of the most studied models to extend the Standard Model (SM) of Particle Physics beyond the electroweak scale. In many supersymmetric models, the lightest supersymmetric particle is stable and can be a suitable candidate for dark matter.\\ This dissertation summarises a search for supersymmetric phenomena produced via the strong or the electroweak interaction leading to final states with two leptons (electrons or muons) of the same electric charge, or three leptons, jets and missing transverse momentum. While the same-sign or three leptons signature is present in many SUSY scenarios, SM processes leading to such events have very small production rates. Therefore, this analysis benefits from a small SM background in the signal regions leading to a good sensitivity especially in SUSY scenarios with compressed mass spectra or in which the R-parity is not conserved. The search was performed with cut-and-count analyses exploiting the full dataset recorded with the ATLAS detector at the Large Hadron Collider during the years 2015 and 2016, corresponding to a total integrated luminosity of 36.1 fb$^{-1}$. No significant excess above the Standard Model expectations is observed. The results are interpreted in several simplified supersymmetric models featuring R-parity conservation or R-parity violation, extending the exclusion limits from previous searches.\\ Since no sign of SUSY particles has been observed, this dissertation presents prospects for a search for compressed electroweakino production. This supersymmetric scenario is particularly challenging for LHC experiments since the products of the decay chain have low energies and are therefore difficult to detect. Results are obtained with a parameterised simulation of the ATLAS detector performances at a centre-of-mass energy of 14 TeV and for an integrated luminosity of 3000 fb$^{-1}$.\\