The first search is presented for vector-like leptons (VLLs) in the context of the "4321 model", an ultraviolet-complete model with the potential to explain existing B physics measurements that are in tension with standard model predictions. The analyzed data, corresponding to an integrated luminosity of 96.5fb^-1, were recorded in 2017 and 2018 with the CMS detector at the LHC in proton-proton collisions at √s=13 TeV. Final states with ≥3 b -tagged jets and two third-generation leptons (ττ, τν_τ, or ν_τν_τ) are considered. Upper limits are derived on the VLL production cross section in the VLL mass range 500-1050 GeV. The maximum likelihood fit prefers the presence of signal at the level of 2.8 standard deviations, for a representative VLL mass point of 600 GeV. As a consequence, the observed upper limits are approximately double the expected limits.