  A search is presented for vector-like T and B quark-antiquark pairs produced
in proton-proton collisions at a center-of-mass energy of 13 TeV. Data were
collected by the CMS experiment at the CERN LHC in 2016-2018, with an
integrated luminosity of 138 fb$^{-1}$. Events are separated into
single-lepton, same-sign charge dilepton, and multilepton channels. In the
analysis of the single-lepton channel a multilayer neural network and jet
identification techniques are employed to select signal events, while the
same-sign dilepton and multilepton channels rely on the high-energy signature
of the signal to distinguish it from standard model backgrounds. The data are
consistent with standard model background predictions, and the production of
vector-like quark pairs is excluded at 95% confidence level for T quark masses
up to 1.54 TeV and B quark masses up to 1.56 TeV, depending on the branching
fractions assumed, with maximal sensitivity to decay modes that include
multiple top quarks. The limits obtained in this search are the strongest
limits to date for $\mathrm{T\overline{T}}$ production, excluding masses below
1.48 TeV for all decays to third generation quarks, and are the strongest
limits to date for $\mathrm{B\overline{B}}$ production with B quark decays to
tW.
