How to make cables sag when an object travels over it

That would definitely be the way to go about it. And the ropes can indeed overlap without a problem.

But there is a thing to change from the design I explained previously. I had the ropes parented to the lift, which isn’t ideal in this case. Parent each rope to its corresponding point (A-B to A, B-A to B, etc.).
That way you don’t need to change the parent of any constraints. When switching to the B-C and C-B ropes, just change their Attachment1 property, they can stay parented to their point.

So every rope’s Attachment0 property should always be its starter point, and the Attachment1 should either be the lift or the opposing point, depending on if the lift is there or not.

3 Likes