It is an apparently well known result that if one has a 1-parameter family of smooth Calabi-Yau 3-folds which acquires a node at a boundary point, then there is a vanishing lagrangian 3-sphere, and the geometrical monodromy is a Dehn-twist along this sphere whose effect on the homology of our base fiber is given by the classical Picard-Lefschetz formula $$\alpha \mapsto \alpha-(\delta\cdot \alpha) \delta,$$ where $\delta$ is the homology class of the vanishing 3-sphere. (This formula or an analogue of it actually holds in much more general families than just CY 3-folds, but that's the case I'm interested in). For a modern reference for the above result, see Chapter 3 of Looijenga's $\textit{Isolated Singular Points on Complete Intersections}$.

My question is whether there is a known analogue for the case when the family in question acquires more than one $A_1$-singularity. For example, if the smooth family acquires 4 nodes, is there a known formula for the monodromy action around such a fiber for Calabi-Yau 3-folds?

If no formula exists, is there any sense for what it's matrix might look like, roughly? Do we know, for example, that $Rank(S-1)=1$, where $S$ is the monodromy action and $1$ is the identity matrix?