Sphere / Sphere Intersection ?

My coding abilities are very limited. 

I have numerous swept Arc's (converted to mesh) that I need to find the intsection of.  the Boolean Intersection components work fine for just two mesh objects, but as soon as I add the third mesh, the results are not as expected.

Every mesh object has randomly varing depths (Z), so it makes it interesting to find the intersection.

Are there any exsisting scripts/components that would find the intersection so I can rebuild these meshes ?