Bring 6 quarts water to boil and set up ice bath.
Cook shrimp for 1 1/2 minutes and plunge into ice bath. Cook calamari 1 minute and do the same. Cook lobster for 8 minutes and then cool in ice bath.
In a large saute pan, place mussels and clams with 1 cup of water and bring to a boil. Cover and steam, removing each shellfish as it opens until they are all done. Discard those shellfish which do not open. Keeping each open shellfish separate, dress each individually with 1 to 2 tablespoons extra virgin olive oil, a touch of lemon juice, a pinch of chilies and 1 to 2 tablespoons parsley. Do the same with the crab meat. Arrange all the seafood on a big platter. Garnish with lemon wedges and serve.