  We report on our recent comparison of various theoretical approaches to
predict fiducial signatures for $pp\to t\bar{t}W$ in the $3\ell$ decay channel
at $\mathcal{O}(\alpha_s^3\alpha^6)$ and $\mathcal{O}(\alpha_s\alpha^8)$. The
comparison includes fixed-order predictions including full off-shell effects as
well as predictions based only on the double-resonant contributions by
employing the Narrow-Width-Approximation. Furthermore, we include parton-shower
matched predictions using the MG5 and POWHEG-BOX frameworks.
