Heat oil in a large saucepan over medium-high heat. Saute onion and bell pepper in hot oil until tender, about 5 minutes; add garlic and continue to saute until garlic is fragrant, about 1 minute. Transfer mixture to a large stockpot.
Stir tomatoes, chicken broth, white wine, tomato paste, parsley, basil, oregano, red pepper flakes, and black pepper with the onion mixture in the stockpot; bring to a boil, cover the pot, reduce heat to medium-low, and simmer until the tomatoes are softened, about 15 minutes.
Stir shrimp and cod chunks into the tomato mixture. Arrange clams and mussels in the liquid so they are partially submerged. Cover pot again and continue cooking until the clams and mussels open, 7 to 10 minutes.
