A bstract A measurement is performed of the cross section of top quark pair production in association with a W or Z boson using proton-proton collisions at a center-of-mass energy of 13 TeV at the LHC. The data sample corresponds to an integrated luminosity of 35.9 fb −1 , collected by the CMS experiment in 2016. The measurement is performed in the same-sign dilepton, three- and four-lepton final states. The production cross sections are measured to be $$ \sigma \left(\mathrm{t}\overline{\mathrm{t}}\mathrm{W}\right)={0.77}_{-0.11}^{+0.12}{\left(\mathrm{stat}\right)}_{-0.12}^{+0.13}\left(\mathrm{syst}\right)\mathrm{p}\mathrm{b} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>σ</mml:mi> <mml:mfenced> <mml:mrow> <mml:mi>t</mml:mi> <mml:mover> <mml:mi>t</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>W</mml:mi> </mml:mrow> </mml:mfenced> <mml:mo>=</mml:mo> <mml:msubsup> <mml:mn>0.77</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.11</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.12</mml:mn> </mml:mrow> </mml:msubsup> <mml:msubsup> <mml:mfenced> <mml:mi>stat</mml:mi> </mml:mfenced> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.12</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.13</mml:mn> </mml:mrow> </mml:msubsup> <mml:mfenced> <mml:mi>syst</mml:mi> </mml:mfenced> <mml:mi>p</mml:mi> <mml:mi>b</mml:mi> </mml:math> and $$ \sigma \left(\mathrm{t}\overline{\mathrm{t}}\mathrm{Z}\right)={0.99}_{-0.08}^{+0.09}{\left(\mathrm{stat}\right)}_{-0.10}^{+0.12}\left(\mathrm{syst}\right)\mathrm{p}\mathrm{b} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>σ</mml:mi> <mml:mfenced> <mml:mrow> <mml:mi>t</mml:mi> <mml:mover> <mml:mi>t</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>Z</mml:mi> </mml:mrow> </mml:mfenced> <mml:mo>=</mml:mo> <mml:msubsup> <mml:mn>0.99</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.08</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.09</mml:mn> </mml:mrow> </mml:msubsup> <mml:msubsup> <mml:mfenced> <mml:mi>stat</mml:mi> </mml:mfenced> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.10</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.12</mml:mn> </mml:mrow> </mml:msubsup> <mml:mfenced> <mml:mi>syst</mml:mi> </mml:mfenced> <mml:mi>p</mml:mi> <mml:mi>b</mml:mi> </mml:math> . The expected (observed) signal significance for the $$ \mathrm{t}\overline{\mathrm{t}}\mathrm{W} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>t</mml:mi> <mml:mover> <mml:mi>t</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>W</mml:mi> </mml:math> production in same-sign dilepton channel is found to be 4.5 (5.3) standard deviations, while for the $$ \mathrm{t}\overline{\mathrm{t}}\mathrm{Z} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>t</mml:mi> <mml:mover> <mml:mi>t</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>Z</mml:mi> </mml:math> production in three- and four-lepton channels both the expected and the observed significances are found to be in excess of 5 standard deviations. The results are in agreement with the standard model predictions and are used to constrain the Wilson coefficients for eight dimension-six operators describing new interactions that would modify $$ \mathrm{t}\overline{\mathrm{t}}\mathrm{W} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>t</mml:mi> <mml:mover> <mml:mi>t</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>W</mml:mi> </mml:math> and $$ \mathrm{t}\overline{\mathrm{t}}\mathrm{Z} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>t</mml:mi> <mml:mover> <mml:mi>t</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>Z</mml:mi> </mml:math> production.