Mix basil, cilantro, parsley, shallots, and garlic with fish, scallops, and shrimp. Set aside.
Bring broth to a boil in a 5- to 6-quart pan over high heat. Add clams and lobster. Cover and simmer until clams open and lobster is barely opaque in thickest part (cut to test), 5 to 10 minutes. As clams open, lift them from the simmering broth with a slotted spoon and keep warm.
After 10 minutes, add seasoned fish, scallops, and shrimp to simmering broth. Bring to a boil over high heat, then tightly cover pan and remove from heat. Let stand until shrimp, scallops, and fish are barely opaque in thickest part (cut to test), 3 to 5 minutes. Use in bouillabaisse or, with a slotted spoon, divide seafood equally among wide, shallow bowls. Over high heat, bring broth to boiling, then ladle into bowls.