The results of a search for supersymmetric particles in final states with four or more leptons (electrons or muons) and missing transverse momentum with the ATLAS detector are presented. The analysis uses a sample corresponding to an integrated luminosity of 2.06 fb−1 of proton-proton data recorded in 2011 at a centre-of-mass energy of 7 TeV. With an inclusive selection four events are observed, while 1.7±0.9 are expected from Standard Model processes. After applying a Z boson veto for leptons pairs with the same flavour and opposite charge, no events are observed for 0.7±0.8 events expected. Within the selection acceptance, we determine 95% C.L. visible cross-section upper limits for new phenomena of 3.5 fb and 1.5 fb for the selections without and with the Z-veto, respectively.