Split Curves on Same list at their intersection

Helllo everyone,

I have a tree of curves and the branches contains x nr of curves. Some branches have intersection and some dont.

I managed to separate the branches that have from the ones that dont, but now I am having trouble splitting the curve inside the branch. I am using the "multiple curves" component, but I cant achieve what I want:

Right current curves, Left intended.

Thanks for any help.