The biggest bodied P-basses would probably be early 50's reproductions with 1/4" edge radius, and no belly/arm contours.
Benavente used to offer this, calling it the "51 model". I have a pair of 5 string 51 models (below), they were also available in 4 string (and maybe 6). The blocky body does appear larger than a normal P-bass. They are also weighty, and have big chunky necks to match (a good thing in my book). I no longer see them on the website (www.benaventeguitars.com
) -- the relic P-bass shown on the "Classic" page has contouring and a 1/2" edge radius making it similar to modern P-basses. But you could contact the shop to see if they can make you a 51 model.