The large dataset accumulated by the ATLAS detector at a centre of mass energy of $\sqrt{s}=13\,$GeV provided at the LHC allows the study of rare SM top quark production processes. The observation of associated production of top quarks has provided the first direct measurement of the top quark electroweak couplings with neutral gauge bosons and the first access to the four-top-quark production process. Using the data set collected during Run 2 of the LHC between 2015 and 2018, and amounting to $139\,\mathrm{fb}^{-1}$ of proton-proton collisions, the ATLAS experiment has observed ttX production, with X=$\gamma$, Z, H and single top quark production with X=$\gamma$, Z, W. In this contribution, new differential measurements of the $t\bar{t}Z$ and $t\bar{t}\gamma$ cross-sections are presented, as well as inclusive cross-section measurements of $tZq$ and $tq\gamma$ production. The latter is a brand new result, which corresponds to the first observation of this process. Results are also presented from the search for four-top-quark production, where the combination of several searches in various channels leads to strong (4.7 $\sigma$) evidence for the existence of this elusive process.