A search for new phenomena in final states characterized by high jet multiplicity, an isolated lepton (electron or muon) and either zero or at least three b-tagged jets is presented. The search uses 36.1 fb−1 of √s=13 TeV proton-proton collision data collected by the ATLAS experiment at the Large Hadron Collider in 2015 and 2016. The dominant sources of background are estimated using parameterized extrapolations, based on observables at medium jet multiplicity, to predict the b-tagged jet multiplicity distribution at the higher jet multiplicities used in the search. No significant excess over the Standard Model expectation is observed and 95% confidence-level limits are extracted constraining four simplified models of R-parity-violating supersymmetry that feature either gluino or top-squark pair production. The exclusion limits reach as high as 2.1 TeV in gluino mass and 1.2 TeV in top-squark mass in the models considered. In addition, an upper limit is set on the cross-section for Standard Model tt¯tt¯ production of 60 fb (6.5 × the Standard Model prediction) at 95% confidence level. Finally, model-independent limits are set on the contribution from new phenomena to the signal-region yields.