Abstract The standard model (SM) production of four top quarks ($$\text {t} {}{\overline{\text {t}}} \text {t} {}{\overline{\text {t}}} $$ tt¯tt¯ ) in proton–proton collisions is studied by the CMS Collaboration. The data sample, collected during the 2016–2018 data taking of the LHC, corresponds to an integrated luminosity of 137$$\,\text {fb}^{-1}$$ fb-1 at a center-of-mass energy of 13$$\,\text {TeV}$$ TeV . The events are required to contain two same-sign charged leptons (electrons or muons) or at least three leptons, and jets. The observed and expected significances for the $$\text {t} {}{\overline{\text {t}}} \text {t} {}{\overline{\text {t}}} $$ tt¯tt¯ signal are respectively 2.6 and 2.7 standard deviations, and the $$\text {t} {}{\overline{\text {t}}} \text {t} {}{\overline{\text {t}}} $$ tt¯tt¯ cross section is measured to be $$12.6^{+5.8}_{-5.2}\,\text {fb} $$ 12.6-5.2+5.8fb . The results are used to constrain the Yukawa coupling of the top quark to the Higgs boson, $$y_{\text {t}}$$ yt , yielding a limit of $$|y_{\text {t}}/y_{\text {t}}^{\mathrm {SM}} | < 1.7$$ |yt/ytSM|<1.7 at $$95\%$$ 95% confidence level, where $$y_{\text {t}}^{\mathrm {SM}}$$ ytSM is the SM value of $$y_{\text {t}}$$ yt . They are also used to constrain the oblique parameter of the Higgs boson in an effective field theory framework, $$\hat{H}<0.12$$ H^<0.12 . Limits are set on the production of a heavy scalar or pseudoscalar boson in Type-II two-Higgs-doublet and simplified dark matter models, with exclusion limits reaching 350–470$$\,\text {GeV}$$ GeV and 350–550$$\,\text {GeV}$$ GeV for scalar and pseudoscalar bosons, respectively. Upper bounds are also set on couplings of the top quark to new light particles.