In a large dutch oven, heat the olive oil. Add the diced yellow onion and saute until translucent. Add the minced garlic and saute until fragrant, about 1 minute longer.
Add the lima beans, corn, diced tomatoes, and stock. Bring to a boil. Reduce the heat, cover and simmer for 20 minutes until the vegetables are tender.
Add the pulled pork, shredded chicken, BBQ sauce, and salt and pepper to taste. Stir to combine and simmer for 15 more minutes. Remove from the heat and adjust seasoning to taste. Serve hot.