A search for physics beyond the standard model in events with at least three leptons and any number of jets is presented. The data sample corresponds to 35 inverse picobarns of integrated luminosity in pp collisions at sqrt(s) = 7 TeV collected by the CMS experiment at the LHC. A number of exclusive multileptonic channels are investigated and standard model backgrounds are suppressed by requiring sufficient missing transverse energy, invariant mass inconsistent with that of the Z boson, or high jet activity. Control samples in data are used to ascertain the robustness of background evaluation techniques and to minimise the reliance on simulation. The observations are consistent with background expectations. These results constrain previously unexplored regions of supersymmetric parameter space.