  We classify, up to fiberwise symplectomorphisms, a saturated neighborhood of
a singular fiber of an integrable system (which is proper onto its image and
has connected fibers) containing $k > 1$ focus-focus critical points. Our
result shows that there is a one-to-one correspondence between such
neighborhoods and $k$ formal power series, up to a $(\mathbb{Z}_2 \times
D_k)$-action, where $D_k$ is the $k$-th dihedral group. The $k$ formal power
series determine the dynamical behavior of the Hamiltonian vector fields
associated to the components of the momentum map on the symplectic manifold
$(M,\omega)$ near the singular fiber containing the $k$ focus-focus critical
points. This proves a conjecture of San Vu Ngoc from 2002.
