We compare fixed order and parton shower matched predictions for the process ${pp\rightarrow \ell^+\nu_{\ell} \ell^-\bar{\nu}_{\ell} \ell^{\pm}\overset{\textbf{\fontsize{2pt}{2pt}\selectfont(---)}}{\nu}_{\ell} b\bar{b}+X}$ at NLO in QCD, including the orders $\mathcal{O}(\alpha_s^3\alpha^6)$ and $\mathcal{O}(\alpha_s\alpha^8)$. The comparison is performed at the integrated and differential fiducial level at the LHC with $\sqrt{s}=13$ TeV. In the absence of parton shower matching procedure that includes the full off-shell effects for this process at NLO in QCD, we propose a new prescription. It enables the inclusion of approximate full off-shell effects to currently available parton shower matched predictions at NLO in QCD.