jats:titleAbstract</jats:title>jats:pA search for leptoquark pair production decaying into jats:inline-formulajats:alternativesjats:tex-math$$te^- \bar{t}e^+$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:mrow mml:mit</mml:mi> mml:msup mml:mie</mml:mi> mml:mo-</mml:mo> </mml:msup> mml:mover mml:mrow mml:mit</mml:mi> </mml:mrow> mml:mrow mml:mo¯</mml:mo> </mml:mrow> </mml:mover> mml:msup mml:mie</mml:mi> mml:mo+</mml:mo> </mml:msup> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> or jats:inline-formulajats:alternativesjats:tex-math$$t\mu ^- \bar{t}\mu ^+$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:mrow mml:mit</mml:mi> mml:msup mml:miμ</mml:mi> mml:mo-</mml:mo> </mml:msup> mml:mover mml:mrow mml:mit</mml:mi> </mml:mrow> mml:mrow mml:mo¯</mml:mo> </mml:mrow> </mml:mover> mml:msup mml:miμ</mml:mi> mml:mo+</mml:mo> </mml:msup> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> in final states with multiple leptons is presented. The search is based on a dataset of jats:italicpp</jats:italic> collisions at jats:inline-formulajats:alternativesjats:tex-math$$\sqrt{s}=13~\text {TeV} $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:mrow mml:msqrt mml:mis</mml:mi> </mml:msqrt> mml:mo=</mml:mo> mml:mn13</mml:mn> mml:mspace/ mml:mtextTeV</mml:mtext> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> recorded with the ATLAS detector during Run 2 of the Large Hadron Collider, corresponding to an integrated luminosity of 139 fbjats:inline-formulajats:alternativesjats:tex-math$$^{-1}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:mmultiscripts mml:mrow/ mml:mrow/ mml:mrow mml:mo-</mml:mo> mml:mn1</mml:mn> </mml:mrow> </mml:mmultiscripts> </mml:math></jats:alternatives></jats:inline-formula>. Four signal regions, with the requirement of at least three light leptons (electron or muon) and at least two jets out of which at least one jet is identified as coming from a jats:italicb</jats:italic>-hadron, are considered based on the number of leptons of a given flavour. The main background processes are estimated using dedicated control regions in a simultaneous fit with the signal regions to data. No excess above the Standard Model background prediction is observed and 95% confidence level limits on the production cross section times branching ratio are derived as a function of the leptoquark mass. Under the assumption of exclusive decays into jats:inline-formulajats:alternativesjats:tex-math$$te^{-}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:mrow mml:mit</mml:mi> mml:msup mml:mie</mml:mi> mml:mo-</mml:mo> </mml:msup> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> (jats:inline-formulajats:alternativesjats:tex-math$$t\mu ^{-}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:mrow mml:mit</mml:mi> mml:msup mml:miμ</mml:mi> mml:mo-</mml:mo> </mml:msup> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula>), the corresponding lower limit on the scalar mixed-generation leptoquark mass jats:inline-formulajats:alternativesjats:tex-math$$m_{\textrm{LQ}{\textrm{mix}}^{\textrm{d}}}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:msub mml:mim</mml:mi> mml:msubsup mml:mtextLQ</mml:mtext> mml:mrow mml:mtextmix</mml:mtext> </mml:mrow> mml:mtextd</mml:mtext> </mml:msubsup> </mml:msub> </mml:math></jats:alternatives></jats:inline-formula> is at 1.58 (1.59) TeV and on the vector leptoquark mass jats:inline-formulajats:alternativesjats:tex-math$$m{{\tilde{U}}_1}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:msub mml:mim</mml:mi> mml:msub mml:mover mml:miU</mml:mi> mml:mo~</mml:mo> </mml:mover> mml:mn1</mml:mn> </mml:msub> </mml:msub> </mml:math></jats:alternatives></jats:inline-formula> at 1.67 (1.67) TeV in the minimal coupling scenario and at 1.95 (1.95) TeV in the Yang–Mills scenario.</jats:p>