Fill a large pot halfway with lightly salted water; bring to a boil. Add onions and carrots; cook until slightly tender, 10 minutes. Add potatoes; cook until tender, 15 to 20 minutes.
Stir in salmon, cod, scallops, shrimp, lobster, and crab; cook over medium heat until salmon and cod are firm but chunks are still slightly translucent in the center, about 10 minutes. Drain half the water from the pot and add clams, heavy cream, and half-and-half. Place butter chunks atop the soup; season with salt and black pepper. Cover and simmer, stirring occasionally, until salmon and cod are fully cooked and flake easily with a fork, about 30 minutes.
