Is there a baseplate with connections on the bottom?
You can certainly combine a number of LEGO parts to build the sort of element you are hoping for. If you want just one part to do this as simply as possible, I'd recommend a 16x16 plate:



This part is about 5 inches by 5 inches and has studs on top and antistuds underneath. You can find it on Bricklink:

http://alpha.bricklink.com/pages/clone/catalogitem.page?P=91405

There have also been some large bricks (up to 12x24) that might work for you: