Steenbrink in his paper "Limit of Hodge Structures", (supplemented by the book "Mixed Hodge Structures" by Peters and Steenbrink) discuss the limit mixed Hodge structures for a fibration over the unit disc $\Delta \subset \mathbb{C}$, i.e. a fibration $$\pi: X \rightarrow \Delta$$ whose fibers are projective varieties and the only singular fiber is over 0, which is a reduced divisor with smooth normal crossing components.

**Question**: Does Steenbrink's construction in his paper (or book) work in the general case i.e. for a fibration
$$\pi: X \rightarrow \Delta^n$$
I guess this also involves the issues with "simultaneous semi-stable reduction" of this family, which has been discussed in the paper "A tour of stable reduction with applications".