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We present measurements of the branching fractions and charge asymmetries of $B$ decays to all ${D}^{(*)}{\overline{D}}^{(*)}$ modes. Using $232\ifmmode\times\else\texttimes\fi{}{10}^{6}$ $B\overline{B}$ pairs recorded on the $\mathit{\ensuremath{\Upsilon}}(4S)$ resonance by the BABAR detector at the ${e}^{+}{e}^{\ensuremath{-}}$ asymmetric $B$ factory PEP-II at the Stanford Linear Accelerator Center, we measure the branching fractions $\mathcal{B}({B}^{0}\ensuremath{\rightarrow}{D}^{*+}{D}^{*\ensuremath{-}})=(8.1\ifmmode\pm\else\textpm\fi{}0.6\ifmmode\pm\else\textpm\fi{}1.0)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$, $\mathcal{B}({B}^{0}\ensuremath{\rightarrow}{D}^{*\ifmmode\pm\else\textpm\fi{}}{D}^{\ensuremath{\mp}})=(5.7\ifmmode\pm\else\textpm\fi{}0.7\ifmmode\pm\else\textpm\fi{}0.7)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$, $\mathcal{B}({B}^{0}\ensuremath{\rightarrow}{D}^{+}{D}^{\ensuremath{-}})=(2.8\ifmmode\pm\else\textpm\fi{}0.4\ifmmode\pm\else\textpm\fi{}0.5)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$, $\mathcal{B}({B}^{+}\ensuremath{\rightarrow}{D}^{*+}{\overline{D}}^{*0})=(8.1\ifmmode\pm\else\textpm\fi{}1.2\ifmmode\pm\else\textpm\fi{}1.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$, $\mathcal{B}({B}^{+}\ensuremath{\rightarrow}{D}^{*+}{\overline{D}}^{0})=(3.6\ifmmode\pm\else\textpm\fi{}0.5\ifmmode\pm\else\textpm\fi{}0.4)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$, $\mathcal{B}({B}^{+}\ensuremath{\rightarrow}{D}^{+}{\overline{D}}^{*0})=(6.3\ifmmode\pm\else\textpm\fi{}1.4\ifmmode\pm\else\textpm\fi{}1.0)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$, and $\mathcal{B}({B}^{+}\ensuremath{\rightarrow}{D}^{+}{\overline{D}}^{0})=(3.8\ifmmode\pm\else\textpm\fi{}0.6\ifmmode\pm\else\textpm\fi{}0.5)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$, where in each case the first uncertainty is statistical and the second systematic. We also determine the limits $\mathcal{B}({B}^{0}\ensuremath{\rightarrow}{D}^{*0}{\overline{D}}^{*0})<0.9\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$, $\mathcal{B}({B}^{0}\ensuremath{\rightarrow}{D}^{*0}{\overline{D}}^{0})<2.9\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$, and $\mathcal{B}({B}^{0}\ensuremath{\rightarrow}{D}^{0}{\overline{D}}^{0})<0.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$, each at 90% confidence level. All decays above denote either member of a charge-conjugate pair. We also determine the $CP$-violating charge asymmetries $\mathcal{A}({B}^{0}\ensuremath{\rightarrow}{D}^{*\ifmmode\pm\else\textpm\fi{}}{D}^{\ensuremath{\mp}})=0.03\ifmmode\pm\else\textpm\fi{}0.10\ifmmode\pm\else\textpm\fi{}0.02$, $\mathcal{A}({B}^{+}\ensuremath{\rightarrow}{D}^{*+}{\overline{D}}^{*0})=\ensuremath{-}0.15\ifmmode\pm\else\textpm\fi{}0.11\ifmmode\pm\else\textpm\fi{}0.02$, $\mathcal{A}({B}^{+}\ensuremath{\rightarrow}{D}^{*+}{\overline{D}}^{0})=\ensuremath{-}0.06\ifmmode\pm\else\textpm\fi{}0.13\ifmmode\pm\else\textpm\fi{}0.02$, $\mathcal{A}({B}^{+}\ensuremath{\rightarrow}{D}^{+}{\overline{D}}^{*0})=0.13\ifmmode\pm\else\textpm\fi{}0.18\ifmmode\pm\else\textpm\fi{}0.04$, and $\mathcal{A}({B}^{+}\ensuremath{\rightarrow}{D}^{+}{\overline{D}}^{0})=\ensuremath{-}0.13\ifmmode\pm\else\textpm\fi{}0.14\ifmmode\pm\else\textpm\fi{}0.02$. Additionally, when we combine these results with information from time-dependent $CP$ asymmetries in ${B}^{0}\ensuremath{\rightarrow}{D}^{(*)+}{D}^{(*)\ensuremath{-}}$ decays and world-averaged branching fractions of $B$ decays to ${D}_{s}^{(*)}{\overline{D}}^{(*)}$ modes, we find the Cabibbo-Kobayashi-Maskawa phase $\ensuremath{\gamma}$ is favored to lie in the range (0.07--2.77) radians (with a $+0$ or $+\ensuremath{\pi}$ radians ambiguity) at 68% confidence level.

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