We present a selection of results from our recent study of $pp\to t\bar{t}W^\pm$
production matched to partons showers at NLO QCD at the LHC. Theoretical
predictions are obtained at perturbative orders $\mathcal{O}(\alpha_s^3\alpha)$
and $\mathcal{O}(\alpha_s\alpha^3)$, where the different contributions are
studied first separately at the inclusive level before being combined within a
realistic two same-sign lepton signature. We investigate in detail uncertainties
originating from missing higher-order corrections and from the parton-shower
matching scheme employed.