Results from a search for supersymmetry in events with four or more leptons including electrons, muons and taus are presented. The analysis uses a data sample corresponding to 20.3  fb−1 of proton-proton collisions delivered by the Large Hadron Collider at s√=8  TeV and recorded by the ATLAS detector. Signal regions are designed to target supersymmetric scenarios that can be either enriched in or depleted of events involving the production of a Z boson. No significant deviations are observed in data from standard model predictions and results are used to set upper limits on the event yields from processes beyond the standard model. Exclusion limits at the 95% confidence level on the masses of relevant supersymmetric particles are obtained. In R-parity-violating simplified models with decays of the lightest supersymmetric particle to electrons and muons, limits of 1350 and 750 GeV are placed on gluino and chargino masses, respectively. In R-parity-conserving simplified models with heavy neutralinos decaying to a massless lightest supersymmetric particle, heavy neutralino masses up to 620 GeV are excluded. Limits are also placed on other supersymmetric scenarios.