If you check this page, you'll see Heather's recommendations for how to begin adding other food after a few days on the Break The Cycle diet.
As a general rule, the tougher a food is, the harder it is on IBS, so stuff like popcorn, nuts, and bacon are going to be for later, when he's more stable. In addition, nuts and bacon are relatively high in fat. Even green beans can be tough - think of the "strings" in them.
Some people on the Board cannot tolerate popcorn because of the hulls. If it's a particular favorite of your son's, try doing a search on "hull popcorn" and see if you can find some of the information posted on where to buy popcorn without hulls. Even then you should still be cautious - it's an insoluble fiber even without the hulls.
Also, be sure to "wrap" protein and insoluble fiber in lots and lots of soluble fiber. In the beginning it's easiest if you hide the unsafe stuff inside safe stuff, which is why Heather's recommendations for easing off the BTC diet include stuff like fruit and vegetable breads and smoothies. If you son is eager for "good stuff" after a few days of just soluble fiber, foods like the pumpkin apple spice bread and Heather's Chocolate Silk Pudding should be right up his alley. And don't forget angel food cake.
It's very encouraging that the BTC diet made your son feel better. It seems like you're on the right track. Good luck going forward.
-------------------- [Research tells us fourteen out of any ten individuals likes chocolate. - Sandra Boynton]