Yes, John R, Henry H and Alvin Gregorio,
All these head me in the right direction.
However, an added complexity I didn't yet mention is that I actually am pulling 4 surfaces at once.
I have a cylinder that's sliced in half, down the straight axis. Half of the cylinder has a channel in it and the other half has a rail. The 2 half-cylinders fit together forming a clam-shell, where the rail on one fits inside the channel on the other. Then, the connecting edges must both be pulled inward, after which the rail on one must fit into the channel on the other.
The attachment shows the idea of what I need to do, implemented using the Rail Sweep tool. The channel, in the pic is correct, however, because the Rail Sweep is moving a 2 dimensional profile through a path, one dimension is being kept rigid. What I really need, is to place the channel (and rail) on a 3D set of surfaces, like a cylinder, in a cylinder, in a cylinder, in a cylinder (then pull all these surfaces at once, maintaining the distance between each of them.
(I know you guys like challenges; well it's a challenge to me anyway)