Large interactive tabletops are beneficial for various tasks involving exploration and visualization, but regions of the screen far from users can be difficult to reach. We propose AdapTable; a concept and prototype of a flexible multi-display tabletop that can physically reconfigure its layout, allowing for interaction with difficult-to-reach regions. We conducted a design study where we found users preferred to change screen layouts for full-screen interaction, motivated by reduced physical demands and frustration. We then prototyped AdapTable using four actuated tabletop displays each propelled by a mobile robot, and a touch menu was chosen to control the layout. Finally, we conducted a user study to evaluate how well AdapTable addresses the reaching problem compared with a conventional panning technique. Our findings show that AdapTable provides a more efficient method for complex full-screen interaction.