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A search for new phenomena in events with two same- charge leptons or three leptons and jets identi fi ed as originating from b - quarks in a data sample of 36.1 fb of pp collisions at ps = 13TeV recorded by the ATLAS detector at the Large Hadron Collider is reported. No signi fi cant excess is found and limits are set on vector- like quark, fourtop- quark, and same- sign top- quark pair production. The observed ( expected) 95% CL mass limits for a vector- like T - and B - quark singlet are mT > 0 : 98 ( 0 : 99) TeV and mB > 1 : 00 ( 1 : 01) TeV respectively. Limits on the production of the vector- like T5=3 - quark are also derived considering both pair and single production; in the former case the lower limit on the mass of the T5=3 - quark is ( expected to be) 1.19 ( 1.21) TeV. The Standard Model fourtop- quark production cross- section upper limit is ( expected to be) 69 ( 29) fb. Constraints are also set on exotic four- top- quark production models. Finally, limits are set on samesign top- quark pair production. The upper limit on uu ! tt production is ( expected to be) 89 ( 59) fb for a mediator mass of 1TeV, and a dark- matter interpretation is also derived, excluding a mediator of 3TeV with a dark- sector coupling of 1.0 and a coupling to ordinary matter above 0.31.