Based on 3586 six-pronged events, this work presents results on $\overline{p}p$ annihilation into six and seven pions at 5.7 GeV/c. The production of $\rho$, $\omega$, $A_1$, and $A_2$ resonances in the $\overline{p}p\to 3{\pi }^{+}3{\pi }^{-}{\pi }^0$ channel was observed. Cross sections for the production of the $\rho$ and $\omega$ resonances are given. The partial cross sections for $\overline{p}p\to {\rho }^{0}2{\pi }^{+}2{\pi }^{-}{\pi }^0$ and $\overline{p}p\to \omega 2{\pi }^{+}2{\pi }^{-}$ are compared with other experimental data. That the $\overline{p}p\to \omega 2{\pi }^{+}2{\pi }^{-}$ cross section is small at 5.7 GeV/c shows that this reaction contributes in a rather important manner to the peak observed in the $\overline{p}p\to 3{\pi }^{+}3{\pi }^{-}{\pi }^0$ cross section at an incident $\overline{p}$ momentum of 3 GeV/c. Our data show some indication of bumps in the (${\rho }^0{\pi }^0$), (${\rho }^0{\rho }^0$) mass for seven-pions annihilation where ${\rho }^0$ is defined as a (${\pi }^{+}{\pi }^{-}$) system having a mass combination in the ${\rho }^0$ band. As yet the statistics do not allow us to draw a definite conclusion about these effects. By comparison with other experimental data, it seems that the isotropy of the pion angular distribution in the c.m. system increases with the number of outgoing pions.

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