  The foreseen luminosities for the next LHC runs will enable precise
differential measurements of the associated production of top-antitop pairs
with a W boson. Therefore, providing accurate theory predictions for this
process is needed for realistic final states. We present the first combination
of NLO electroweak and QCD corrections to off-shell ttW$^+$ production in the
three-charged-lepton channel, including non-resonant effects, full
spin-correlations and interferences. Such radiative corrections comprise the
electroweak and QCD corrections to the leading QCD order, and the QCD
corrections to the leading electroweak order.
