What is the biggest base plate available?
The largest official baseplate that I'm aware of is 50x50 modules.



It's only slightly larger than a 48x48, and it's a bit more difficult to use in large setups since most other common baseplates have side lengths that are a multiple of 16, so you might actually be better off with a 48x48 depending on what you are trying to do.

This part hasn't been available since the 70s, but you can still pick it up on Bricklink.

You may be interested in this answer which includes other raised baseplates:

What is the largest single LEGO piece?