Constraining an object to the intersection of two paths

I am trying to constrain the location of an object to the intersection of two curved paths.

In the image below, for example, there are two NURBScurves and a Sphere. I want the Sphere to be automatically centred at the intersection of the curves no matter their exact position or curvature.

Using the ‘Clamp To’ tracking constraint I can successful constrain the Sphere so that it lies at a position along one of the curves:

However, if I introduce a second ‘Clamp To’ constraint for the second curve, the Sphere is clamped to the second curve and not to both (i.e. at the intersection of both lines).

If both paths are orthogonal straight lines the dual constraint is successful, but under other conditions it fails.

Any help would be gratefully received!