In a large pan that's at least 2 inches deep, heat the butter over medium-high heat. Add the onion, garlic, and fish and cook for 1 minute. Add the shrimp and scallops and cook, stirring occasionally and flipping the fish once, about 2 minutes more.
Add the tomato, mussels, clams, and crab and pour the white wine over everything. Add the salt and pepper and sprinkle with the basil. Cover and cook until the clams and mussels start to open, about 4 minutes. (Discard any that don't open.)
Remove from heat and divide the seafood and broth among 4 large shallow soup or pasta bowls. Garnish with basil sprigs and serve.