I sometimes have to set points along the intersection between a surface of one solid and the surface of another, say where a triangular prism pokes through a rectangular one.

I have been unable to get object snaps to work for this scenario. Instead, I have to use the Intersect command to intersect the objects, use object snaps to set a point at the desired intersection of the various objects created by the Intersect command, then delete those objects, leaving the point. This is rather clumsy and error-prone. I'd like an object snap that would let me derive the desired point directly.