This is more of a Photoshop task than anything else. Elegant Grunge's background is made up of several images what are positioned to work together.
This is the main image: http://s0.wp.com/wp-content/themes/pub/elegant-grunge/images/body.png and it repeats in the "Y" direction (vertically). You would have to edit or recreate that image adding however much width you wanted.
Then comes the header area, which is actually made up of several images (unless you don't mind the header image being narrower than the body of the site.
Then comes the footer area which also has an image that has to be recreated or edited.
Most likely after you get into it there would be several more come up that would have to be done as well.
Widening the theme is just a few lines of CSS. The real work is all the Photoshopping. How good are you with image creation and editing?