Submitted to Eur. J. Phys. C. All figures and tables can be found at http://cms-results.web.cern.ch/cms-results/public-results/publications/SUS-16-003 ; see paper for full list of authors ; Results are reported from a search for physics beyond-the-standard-model, such as supersymmetry, in final states with at least three charged leptons, in any combination of electrons or muons. The data sample corresponds to an integrated luminosity of 2.3 inverse femtobarns of proton-proton collisions at sqrt(s) =13 TeV, recorded by the CMS experiment at the LHC in 2015. Two jets are required in each event, providing good sensitivity to strong production of gluinos and squarks. The search regions, sensitive to a range of different supersymmetry scenarios, are defined using the number of jets tagged as originating from bottom quarks, the sum of the magnitudes of the transverse momenta of the jets, the imbalance in the overall transverse momentum in the event, and the invariant mass of opposite-sign, same-flavor lepton pairs. The event yields observed in data are consistent with the expected background contributions from standard model processes. These results are used to exclude regions in parameter space in a variety of simplified models of supersymmetry. In a model with gluino pair production, with subsequent decay into a top quark-antiquark pair and a neutralino, gluinos with masses less than 1175 GeV are excluded for light neutralinos.