  A recent study of $D^0 \to \pi^0 K^+ K^-$ and $D^0 \to K_S \pi^+\pi^-$
describes a flavor-symmetric approach to calculate relative amplitudes and
phases, for characteristic interferences between $D$ decays to a light
pseudoscalar $P$ and a light vector $V$, on Dalitz plots for $D \to PPP$
decays. The flavor-symmetric approach used an earlier fit to $D \to P V$ decay
rates and was found to agree fairly well with experiments for $D^0 \to \pi^0
\pi^+ \pi^-$ but not as well for $D^0 \to \pi^0 K^+ K^-$ and $D^0 \to K_S
\pi^+\pi^-$. The present work extends this investigation to include $D^0 \to
K^- \pi^+ \pi^0$. We use an SU(3) flavor symmetry relationship between ratios
of Cabibbo-favored (CF) $D \to P V$ amplitudes in $D^0 \to K^- \pi^+ \pi^0$ and
ratios of singly- Cabibbo-suppressed (SCS) $D \to P V$ amplitudes in $D^0 \to
\pi^0 K^+ K^-$ and $D^0 \to \pi^0 \pi^+ \pi^-$. We observe that experimental
values for Dalitz plot cross ratios obey this relationship up to discrepancies
noted previously. The need for an updated Dalitz plot analysis of $D^0 \to K^-
\pi^+ \pi^0$ is emphasized.
