Thank you in advance for spending time to think about my problem

One of my script has 2 groups of curves and 4 planes.
I am trying to calculate all intersection points ( preferably I would like to have the results on 4 branches).
I am using holistic cross reference, but the results are only 3 groups of points instead of 4.

but consider that Planes are infinite, so each of those will intersect ALL your lines (and that is why for each plane -in each branch- you are getting 16 different intersection points)

if you want to get only the points that looks like intersecting each plane -visually, in your original image- I would create some planar surfaces over the planes, and use Surface|Line intersection (Surfaces are not infinite )