Put 1 inch of water in a large stockpot and place a metal vegetable steamer fanned open in the bottom. Bring to a boil over high heat. Place potatoes on the steamer, cover the pot and steam for 4 minutes. Reduce the heat slightly, if necessary, to prevent boiling over.
Place lobsters on top of the potatoes; cover and steam for 4 minutes. Place clams and mussels on top of the lobsters and potatoes; cover and continue steaming for 4 minutes more. Place corn on top of the shellfish; cover and continue steaming until the clams have opened and the potatoes are tender, 4 to 8 minutes more.
Arrange the corn, mussels, clams and potatoes on large serving platters. Remove lobster claws and tails by twisting them from the body. Cut the tails lengthwise (see Kitchen Notes). Discard the bodies. Add the split tails and claws to the platters and serve immediately with sauces.
How to Shell a Lobster:1. Grasp claw at the knuckle, near the body. With a firm twist, remove the claw from the body. Repeat with the second claw. 2. To remove claw meat, crack through the claw shell using a pair of kitchen shears. (Alternatively, crack with a lobster cracker.)3. Holding the body in one hand and firmly grasping the tail in the other, twist and gently pull the tail from the body. (Discard the body.)4. Cut the tail in half lengthwise with kitchen shears, starting from the underside. Serve halves in the shell or remove the meat.
