Steenbrink in his paper ["Limit of Hodge Structures"](https://link.springer.com/content/pdf/10.1007/BF01403146.pdf), (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"](https://arxiv.org/pdf/1207.1048.pdf).



A question on Steenbrink's paper, limit of Hodge structures
If $\pi$ is semistable, then Fujisawa, *Limits of Hodge structures in several variables. Compositio (1999)*, does this. You might also look at some later papers by the same author for some refinements. 


