  The coherent transport of $n$ fermions in disordered networks of $l$
single-particle states connected by $k$-body interactions is studied. These
networks are modeled by embedded Gaussian random matrix ensemble (EGE). The
conductance bandwidth as well as the ensemble-averaged total current attain
their maximal values if the system is highly filled $n \sim l-1$ and $k\sim
n/2$. For the cases $k=1$ and $k=n$ the bandwidth is minimal. We show that for
all parameters the transport is enhanced significantly whenever centrosymmetric
ensemble (csEGE) are considered. In this case the transmission shows numerous
resonances of perfect transport. Analyzing the transmission by spectral
decomposition, we find that centrosymmetry induces strong correlations and
enhances the extrema of the distributions. This suppresses destructive
interference effects in the system and thus, causes backscattering-free
transmission resonances which enhance the overall transport. The distribution
of the total current for the csEGE has a very large dominating peak for
$n=l-1$, close to the highest observed currents.
