The Yukawa coupling of the Higgs boson to the top quark is a key parameter of the Standard Model. It can be constrained using the associated production process $pp\rightarrow t\bar{t}H+X$. A search for this process using final states with multiple leptons, primarily targeting the decays $H\rightarrow WW^*$ and $H\rightarrow \tau \tau$, has been performed using the data set recorded by the ATLAS detector in 2015 and 2016 at a center of mass energy $\sqrt{s}$ = 13 TeV. The analysis presented here includes two of the four final states distinguished by the number and flavor of leptons: two same-charge light leptons (e or $\mu$) and no hadronically-decaying $\tau$ lepton candidates ($2\ell0\tau_{\textrm{had}}$) and four light leptons ($4\ell$), the remaining channels not covered being two same-charge light leptons and one hadronically-decaying $\tau$ lepton candidate ($2\ell1\tau_{\textrm{had}}$) and three light leptons ($3\ell$). The different background sources are also presented for each channel considered. The latest best-fit value for the ratio of observed versus Standard Model cross sections is then given as well as an upper limit on this parameter.