The Standard Model of particle physics describes all observed fundamental particles and their interactions, but is incomplete. The ATLAS experiment at the Large Hadron Collider has performed a suite of searches for new fundamental particles predicted by `beyond-the-Standard Model' theories such as supersymmetry (SUSY). As yet, no discoveries have been made, but a range of simplified SUSY scenarios have been excluded. This thesis presents three approaches for enhancing the sensitivity of the ATLAS experiment to the electroweak production of supersymmetric particles.

First, realistic supersymmetric scenarios contain a large number of free parameters and a rich phenomenology which is not captured by the simplified model interpretations provided by typical ATLAS SUSY searches. To address this, several key electroweak SUSY searches are interpreted in the phenomenological Minimal Supersymmetric Standard Model. The complementarity of these searches with additional constraints from beyond ATLAS, such as limits from dark matter experiments, is also discussed. This provides a comprehensive analysis of the sensitivity of ATLAS to electroweak supersymmetry and highlights scenarios that remain uncovered by current searches and constraints.

Second, a statistical combination of three orthogonal searches for the pair-production of charginos is performed. This extends and deepens the existing sensitivity and exclusion power offered by each analysis alone.

Finally, a machine learning method is presented to improve the reconstruction performance of missing transverse momentum ($pTmiss$) – an essential variable in many searches for supersymmetry. Two neural-network-based approaches are compared and their potential to enhance the sensitivity of ATLAS to pMSSM scenarios is evaluated.