If you can afford to use NURBS curves, Polypaths or Beziers with automatic handles, then I would suggest using corresponding points in the reference curves and interpolate between them.

Just sample the position of the reference curves and use a Mix Node to find an interpolated position.

Let's use only two curves. A source curve and a target curve. We are going to add geo nodes to the source curve, to instance it and the interpolate the duplicated splines to the proximity position.

1. Resample the curve and get the closest position of the target curve (with the Proximity Node). Store the target position with the Attribute Capture Node.
2. Instance the curve a few times in place. Capture the instance id and then realize the instances.
3. By calculating captured_id / instance_count we will have a relative value [0, 1) to mix the original point position with the target position.
4. Use the captured target position to mix the positions.

This setup is limited by the geometry proximity, but that was the premise of your questions title.