Brute force is the only way that I know of.
In Visio 2003:
1.Drop a new shape on the "higher" level shape. This will become the "new"
level.
2. One by one, drag each of the other shapes that was connected to the
"higher" level shape and drop on the new shape. Any subordinates of the
shape being moved will follow along.
3. When finished with all the shapes, select "Organization Chart->Relayout"
to clean up the drawing.