Rinse and drain the shrimp and salmon.
Cut the salmon into 2-inch pieces.
Rinse the mussels in cold water, discarding any that are open. With a stiff brush, scrub the mussels to remove dirt and beards. In a large bowl, cover the mussels with water, add 2 tablespoons of salt and let them stand for 5 minutes. Repeat 2 to 3 more times.
Melt butter in a heavy-bottom Dutch oven. Add the olive oil, onions, carrots, celery, potatoes and corn. Sauté over medium-low heat for 15 minutes, stirring occasionally. Stir in flour until smooth.
Stir the seafood stock into sautéed mixture. Bring to a boil, reduce the heat and simmer for 10 minutes.
Add the seafood, cover and simmer until just cooked, 6 to 10 minutes.
Discard any unopened mussels. Stir in the cream and parsley and serve.
*If using cooked shrimp, add in after step 6.