  In arXiv1312.7267, the first non-trivial example of a Poisson manifold of
strong compact type is given. The construction uses the theory of K3 surfaces
and results in a Poisson manifold with leaf space $S^1$. We modify the
construction to obtain a new class of examples. Specifically, we obtain for
each strongly integral affine 2-torus a Poisson manifold of strong compact type
with said torus as leaf space.
