A data sample of events from proton–proton collisions with two isolated same-sign leptons, missing transverse momentum, and jets is studied in a search for signatures of new physics phenomena by the CMS Collaboration at the LHC. The data correspond to an integrated luminosity of 35.9fb⁻¹, and a center-of-mass energy of 13TeV. The properties of the events are consistent with expectations from standard model processes, and no excess yield is observed. Exclusion limits at 95% confidence level are set on cross sections for the pair production of gluinos, squarks, and same-sign top quarks, as well as top-quark associated production of a heavy scalar or pseudoscalar boson decaying to top quarks, and on the standard model production of events with four top quarks. The observed lower mass limits are as high as 1500GeV for gluinos, 830GeV for bottom squarks. The excluded mass range for heavy (pseudo)scalar bosons is 350–360 (350–410)GeV. Additionally, model-independent limits in several topological regions are provided, allowing for further interpretations of the results.