1. In a heavy 6- to 8-quart casserole, heat the oil over high heat until a light haze forms above it. Then add the chopped onions, green pepper and garlic, and cook, stirring occasionally, for 4 to 6 minutes, or until the vegetables are wilted but not brown.
2. Add the tomatoes, tomato paste, wine, ¼ cup of the chopped parsley, saltand a few grindings of pepper, and bring to a boil. Lower the heat, halfcover the casserole and simmer the sauce for about 15 minutes.
3. Add the lobster or crab, baste thoroughly with the sauce and cook over low heat, tightly covered, for about 10 minutes before adding the cutup fish. Cover the casserole again and cook the fish for about 8 minutes, or until it is firm to the touch. Add the shrimp, pushing them beneath the sauce and cook for 3 to 4 minutes, or until they turn pink and are firm.
4. Meanwhile, steam open the clams and mussels by dropping them into a large skillet or casserole filled with about 1 inch of boiling water. Cover the pan tightly and cook the shellfish over moderate heat for 5 to 10 minutes, or until their shells open. Steam those that do not open a little longer, finally discarding any that remain closed.
5. Add the opened mussels and clams (shells and all) to the casserole and baste thoroughly with the sauce. If you like, strain the broth from the steamed shellfish through cheesecloth and add it to the cioppino. However, be careful not to thin the sauce too much.
6. Cover the pan and cook the doppino about 2 to 3 minutes longer, then taste for seasoning. Serve either directly from the casserole or from a large tureen. In either case, sprinkle with the remaining ¼ cup of chopped parsley and accompany the cioppino with hot garlic bread.
