A search for new phenomena in final states with four or more leptons (electrons or muons) is presented. The analysis is based on 4.7 fb^-1 of sqrt(s) = 7 TeV proton-proton collisions delivered by the Large Hadron Collider and recorded with the ATLAS detector. Observations are consistent with Standard Model expectations in two signal regions: one that requires moderate values of missing transverse momentum and another that requires large effective mass. The results are interpreted in a simplified model of R-parity-violating supersymmetry in which a 95% CL exclusion region is set for charged wino masses up to 540 GeV. In an R-parity-violating MSUGRA/CMSSM model, values of m_1/2 up to 820 GeV are excluded for 10<tan(beta)<40.