Into the warmed cioppino sauce, add the clams and mussels. Cover and cook until the clams and mussels just begin to open, about 5 minutes. Add the shrimp and fish. Simmer gently until the fish and shrimp are just cooked through, and the clams and mussels are completely open, stirring gently (discard any clams and mussels that do not open)
Season the stew, to taste, with more pepper, salt and red pepper flakes. Remove the bay leaves.
Meanwhile, cook the spaghetti according to package directions or to desired doneness.
Remove the lid and stir. Remove the shrimp, mussels, clams and fish to a bowl. Drain the pasta, reserving a cup of the pasta water. Add the pasta water to the tomato mixture followed by the spaghetti and stir through the sauce. Season with salt and pepper to taste. Add the chopped parsley, reserving some for garnish, and stir.
To serve, add the pasta to serving bowls, spoon over the tomato sauce and add the shrimp, mussels, clams and fish. Garnish with parsley, basil and a drizzle of olive oil.