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Abstract The rate for Higgs ( $${\mathrm{H}} $$ H ) bosons production in association with either one ( $${\mathrm{t}} {\mathrm{H}} $$ t H ) or two ( $${\mathrm{t}} {{\overline{{{\mathrm{t}}}}}} {\mathrm{H}} $$ t t ¯ H ) top quarks is measured in final states containing multiple electrons, muons, or tau leptons decaying to hadrons and a neutrino, using proton–proton collisions recorded at a center-of-mass energy of $$13\,\text {TeV} $$ 13 TeV by the CMS experiment. The analyzed data correspond to an integrated luminosity of 137 $$\,\text {fb}^{-1}$$ fb - 1 . The analysis is aimed at events that contain $${\mathrm{H}} \rightarrowmore »