Is it possible for an object to follow multiple Clamp To constraints? I am trying to figure out how to get an object to follow two different "Clamp To" constraints. I am not interested in "animation only" solutions, so the Follow Path constraint seems to be out of the question. If there is an entirely different solution than using Clamp To constraints I would love to know about it.
One of my requirements for any solution is that in the end it just works without having to animate it or fiddle with any settings to get the object to follow the path wherever it leads.

I am attaching a Blender Scene file so I can better illustrate the challenge I am facing. When I move the object designated Slide A up and down along the Z axis I would like the object designated as Pin to follow the path designated PinSideToSidePath to constrain Pin's movement only along that path while at the same time following the path designated BezierCircle. Is this possible?



Note: I rotated the animated gif so it would display better. This is a quick animation showing the type of behavior I am trying to create with constraints.
Add a Follow path constraint to the Cylinder, with the bezierCircle object as the target. Enable Follow Curve and set forward to -Z and Up as Y.
(For this to work the curve and the cylinder must have their origins on the same location)

The cylinder follows the path now, as demonstrated here changing the offset values:



Align your Cube.001 sliding object to the cylinder and add a child of constraint, with the cylinder as target. Disable all the boxes except for Location on the Z axis.



To control the slider change the offset values on the follow path constraint for the cylinder.