  This work studies the associated production of a top-quark pair with a $W$,
$Z$, or Higgs boson at the LHC. Predictions for the total cross sections as
well as for several differential distributions of the massive particles in the
final state are provided. These predictions, valid for the LHC operating at
$13$ TeV, include without any approximation all the NLO electroweak and QCD
contributions of $\mathcal{O}(\alpha_s^{i} \alpha^{j+1})$ with $i+j=2,3$. In
addition, the predictions presented here improve upon the NLO QCD results by
adding the effects of soft gluon emission corrections resummed to
next-to-next-to-leading logarithmic accuracy. The residual dependence of the
predictions on scale and PDF choices is analyzed.
