  We study the processes $e^+e^-\to 2(\pi^+\pi^-)\pi^0\pi^0\pi^0\gamma$ and
$2(\pi^+\pi^-)\pi^0\pi^0\eta\gamma$ in which an energetic photon is radiated
from the initial state. The data were collected with the \babar~ detector at
SLAC. About 14\,000 and 4700 events, respectively, are selected from a data
sample corresponding to an integrated luminosity of 469 fb^{-1}. The invariant
mass of the hadronic final state defines the effective \epem center-of-mass
energy. The center-of-mass energies range from threshold to 4.5 GeV. From the
mass spectra, the first ever measurements of the $e^+e^-\to
2(\pi^+\pi^-)\pi^0\pi^0\pi^0$ and the $e^+e^-\to2(\pi^+\pi^-)\pi^0\pi^0\eta$
cross sections are performed. The contributions from
$\omega\pi^+\pi^-\pi^0\pi^0$, $\eta2(\pi^+\pi^-)$, and other intermediate
states are presented. We observe the $J/\psi$ and $\psi(2S)$ in most of these
final states and measure the corresponding branching fractions, many of them
for the first time.
