Animating a point along an individual path

Hey all! I’m trying to select a random number of points from a group of points and animate them along an individual path similar to the illustration below (sorry if the points are a little faint). Any ideas how I can go about doing this?

I would think you could take their current coordinates and shift them w/ a shift CHOP to move them, but maintain the actually contents of the potential positions. Hope this is what you’re looking for!