  CP violation in charm decay was observed in the decays $D^0\rightarrow
P^{\pm}P^{\mp}$ of a $D^0$ meson to two pseudoscalars. When interpreted within
the SM, the results imply that the ratio of the relevant rescattering
amplitudes has a magnitude and phase that are both of $O(1)$. We discuss ways
to probe similar ratios in $D^0\rightarrow V^{\pm}P^{\mp}$ decays, where $V$ is
a vector that decays to two pseudoscalars, from the Dalitz-plot analysis of
time-integrated three-body decays. Compared to two-body decays, three-body
decays have the advantage that the complete system can be solved without the
need for time-dependent CP violation measurements or use of correlated
$D^0$--$\overline{D}^0$ production. We discuss the decays $D^0\rightarrow
\pi^+\pi^-\pi^0$ and $D^0\rightarrow K^+K^-\pi^0$ as examples by considering a
toy model of only two overlapping charged resonances, treating the underlying
pseudo two-body decays in full generality.
