Bring 6 quarts water to a boil in a large stewing pot; add seafood seasoning. Cook potatoes in the seasoned water for 15 minutes.
Bring a separate pot of water to a boil; add seafood seasoning to taste. Cook crab legs until meat is tender, about 10 minutes.
Mix carrots, celery, and onions into potatoes; cook until vegetables are tender, about 10 minutes. Add sausage and corn and continue boiling for 5 minutes more. Add shrimp and transfer crab legs to same pot; cook until shrimp are cooked through and pink, 2 to 3 minutes.