Is there a baseplate with connections on the bottom? Today, I bought a baseplate (10700). Sadly, the female connectors on the back are not "LEGO compatible"...you can't plug any LEGO bricks into them.  I want to build a LEGO cart so dash can pull dot (a big mechanical moving robot can pull a small nonmoving robot). I need to plug the wheels on the bottom of the large brick and a fence to block the little robot in on top. I listed all items in category Bricks on Pick a Brick and found no match.  Similarly for bricklink.

Where can I find a large flat brick (at a minimum 4 inches by 4 inches) so I can build a wagon?

If all else fails, I can super glue some thin bricks together.
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: