  We report measurements of the observed cross sections for $e^+e^-\to\omega
\pi^+\pi^-$, $\omega K^+K^-$, $\omega p\bar p$, $K^+K^-\rho^0\pi^0$,
$K^+K^-\rho^+\pi^-+c.c.$, $K^{*0}K^-\pi^+\pi^0+c.c.$,
$K^{*+}K^-\pi^+\pi^-+c.c.$, $\phi\pi^+\pi^-\pi^0$ and $\Lambda \bar \Lambda
\pi^0$ at $\sqrt s=$ 3.773 and 3.650 GeV. Upper limits (90% C.L.) are given for
observed cross sections and for $\psi(3770)$ decay branching fractions for
production of these final states. These measurements are made by analyzing the
data sets of 17.3 pb$^{-1}$ collected at $\sqrt{s}=3.773$ GeV and 6.5 pb$^{-1}$
collected at $\sqrt{s}=3.650$ GeV with the BES-II detector at the BEPC
collider.
