Trim off and discard tough stems and base of fennel head. Rinse fennel, core, and chop.
In a 6- to 8-quart pan over medium-high heat, stir fennel, oil, onion, garlic, and 2 tablespoons parsley until onion is limp, 8 to 10 minutes.
Add diced tomatoes (including juice), white wine, tomato paste, basil, oregano, and chile flakes. Bring to a boil over high heat. Cover and simmer on low heat until flavors are well blended, about 15 minutes.
Add clams and crab. Cover and bring to a boil over high heat, then reduce heat and simmer, covered, for 5 minutes. Stir in shrimp, cover and simmer, until clams pop open, shrimp turn pink, and crab is hot, 6 to 9 minutes longer; remove seafood as it finishes cooking. Discard clams that do not open. Add salt and pepper to taste. Ladle broth and seafood into wide bowls. Sprinkle with remaining parsley.