Enable Overlapping Shapes in Visio 2013

I have similar problem on Visio 2010 call sequence diagram. The fix is simple - Turning off "Move other shapes away on drop" in "Layout and Routing" tab in the Page Setup.

Enable in Visio 2013 the Developer Mode (Options --> Customize Ribbon --> Select Developer). Next put two rectangles on the page and select both, then on the Developer Tab click on Operations and choose Union or Combine. You can also just put the two rectangles one on the other and they will overlap. You can then group them to make them behave as one object.

This is Union:

This is Combine:

Put one rectangle on top of the other:

If you want a single shape not to re-route (e.g., you want to overlay an object on existing routed shapes or connectors): Select object then select Developer tab > Behavior > Placement tab > Behavior = do not lay out and route around.

See here if you want all shapes not to re-route on the page or other page behavior.