Existence of Lagrangian fibrations for some shifted symplectic structures

Shifted symplectic structures appear most naturally on
moduli spaces (e.g. those of sheaves on Calabi-Yau manifolds).
One would like to know whether presence of a shifted symplectic
structure on a space lets one present the space as the total space
of a Lagrangian fibration. In some cases (e.g. 2-shifted symplectic
structures) this is possible.