A search for new physics is performed using events with two isolated same-sign leptons, two or more jets, and missing transverse momentum. The results are based on a sample of proton-proton collisions at a center-of-mass energy of 13 recorded with the CMS detector at the LHC, corresponding to an integrated luminosity of 2.3 . Multiple search regions are defined by classifying events in terms of missing transverse momentum, the scalar sum of jet transverse momenta, the transverse mass associated with a boson candidate, the number of jets, the number of quark jets, and the transverse momenta of the leptons in the event. The analysis is sensitive to a wide variety of possible signals beyond the standard model. No excess above the standard model background expectation is observed. Constraints are set on various supersymmetric models, with gluinos and bottom squarks excluded for masses up to 1300 and 680, respectively, at the 95 % confidence level. Upper limits on the cross sections for the production of two top quark-antiquark pairs (119) and two same-sign top quarks (1.7) are also obtained. Selection efficiencies and model independent limits are provided to allow further interpretations of the results.