@sherryk - Look at Natural Balance limited ingredients...
https://www.naturalbalanceinc.com/dog-formulas/limited-ingredient-diets. You can search on line for Limited Ingredient foods, but I have used Natural Balance for many years. (but I mix up kibble with different sources, none with corn or beet pulp for sure). I get the small bites 4lb bag and am feeding 2 at this time, cost is $14.39 from Chewy and lasts for about a month for the two. I only get the small bag as it can go bad (as can any kibble) so I know it is pretty fresh. And with Chewy you can set up auto ship for about 1.00 less a bag. I am surprised that green beens is one of you pup's triggers... and I would venture to bet that fed fresh (same with Tomatoes or Pumpkin) they would not be an issue. One of my Basenjis was highly allergic to corn in dog food, but could eat fresh corn on the cob (but not the cob) with no issues....remember that many of the ingredients are processed where as fresh is not...reason many go to raw or home cooked.
In my opinion, Science Diet is not a very good food... almost all of their products have corn and really for any dog, not just a Basenji, corn is a big trigger... This is the main ingredients of the Sensitive Stomach food, Chicken, Brewers Rice, Chicken Meal, Yellow Peas, Cracked Pearled Barley, Whole Grain Sorghum, Egg Product, Chicken Fat, Soybean Oil, Brown Rice, Dried Beet Pulp. Even the venison that is only the 3rd ingredient... not the best in my opinion.
Again I will say that in my opinion Science Diet is not a very good food... and $80 a bag is way overpriced, again in my opinion