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We report on measurements of the decays of $\overline{B}$ mesons into the semileptonic final states $\overline{B} \to D^{(*)} \pi^+\pi^- \ell^-\overline{\nu}$, where $D^{(*)}$ represents a $D$ or $D^*$ meson and $\ell^-$ is an electron or a muon. These measurements are based on $471\times 10^6$ $B\overline{B}$ pairs recorded with the $BABAR$ detector …