  A recent quark-model description of X(3872) as an unquenched $2\,{}^{3\!}P_1$
$c\bar{c}$ state is generalised by now including all relevant meson-meson
configurations, in order to calculate the widths of the experimentally observed
electromagnetic decays $X(3872) \to \gamma J/\psi$ and $X(3872) \to
\gamma\psi(2S)$. Interestingly, the inclusion of additional two-meson channels,
most importantly $D^\pm D^{\star\mp}$, leads to a sizeable increase of the
$c\bar{c}$ probability in the total wave function, although the
$D^0\bar{D}^{\star0}$ component remains the dominant one. As for the
electromagnetic decays, unquenching strongly reduces the $\gamma\psi(2S)$ decay
rate yet even more sharply enhances the $\gamma J/\psi$ rate, resulting in a
decay ratio compatible with one experimental observation but in slight
disagreement with two others. Nevertheless, the results show a dramatic
improvement as compared to a quenched calculation with the same confinement
force and parameters. Concretely, we obtain $\Gamma ( X(3872) \to \gamma
\psi(2S) )=28.9$ keV and $\Gamma ( X(3872) \to \gamma J/\psi)=24.7$ keV, with
branching ratio $\mathcal{R}_{\gamma\psi}=1.17$.
