  Motivated by the reported discrepancies between experimental data and
Standard Model predictions for the branching ratios of the color-allowed decays
$\overline{B}^0 \to D^{(*)+}K^-$ and $\overline{B}^0_s \to D^{(*)+}_s \pi^-$,
we study final-state rescattering effects on $\overline{B}_{(s)}\to
D^{(*)}_{(s)} P$ and $\overline{B}_{(s)}\to D_{(s)} V$, where $P$ ($V$) is a
light pseudoscalar (vector) meson. We consider quasi-elastic rescatterings in
the framework of $SU(3)$ and $U(3)$ flavor symmetries, and find that the
effects cannot explain the measured branching ratios of the color-allowed and
color-suppressed decays simultaneously. We also perform global fits to the
$\overline{B}_{(s)}\to D^{(*)}_{(s)} P$ and $\overline{B}_{(s)}\to D_{(s)} V$
data, allowing for new physics contributions to the Wilson coefficient $a_1$
associated with the color-allowed tree amplitudes. It is shown that the fits
prefer a downward shift of $\mathcal{O}(10\%)$ in $a_1$ even in the presence of
the quasi-elastic rescattering contributions.
