  By analyzing the data sets of 17.3, 6.5 and 1.0 pb$^{-1}$ taken,
respectively, at $\sqrt s= 3.773$, 3.650 and 3.6648 GeV with the BES-II
detector at the BEPC collider, we measure the observed cross sections for
$e^+e^-\to \pi^+\pi^-\pi^0\pi^0$, $K^+K^-\pi^0\pi^0$, $2(\pi^+\pi^-\pi^0)$,
$K^+K^-\pi^+\pi^-\pi^0\pi^0$ and $3(\pi^+\pi^-)\pi^0\pi^0$ at the three energy
points. Based on these cross sections we set the upper limits on the observed
cross sections and the branching fractions for $\psi(3770)$ decay into these
final states at 90% C.L..
