The presentation will focus on a recent search for non-standard Higgs bosons, performed with a data sample collected by the ATLAS experiment at the CERN Large Hadron Collider between 2015 and 2018, and relying on experimental signatures containing multiple leptons. After an introduction to the theoretical and experimental contexts, the discussion will be framed in terms of the search strategies used, with details on the backgrounds present in the regions of interest and the challenges encountered to estimate them precisely. The obtained results will be presented, followed by perspectives for future improvements.