Chef Tip Add the fish to the soup at the end, so it doesn't overcook.
In a saucepan, cover the potatoes with the water and bring to a boil. Cover and cook over moderate heat until the potatoes are tender, about 6 minutes. Remove from the heat and let stand, covered.
Meanwhile, in a large saucepan, heat 1 tablespoon of the oil. Add half of the onion and garlic and cook over moderate heat until softened, 5 minutes. Add the wine and bring to a boil. Add the mussels, cover and cook over moderately high heat until they open, 3 minutes; transfer to a bowl. Add the clams to the saucepan, cover and cook. As the clams open, transfer them to the bowl. Strain and reserve the cooking liquid. Remove the mussels and clams from their shells and coarsely chop them.
Wipe out the saucepan. Add the remaining 1 tablespoon of olive oil and the bacon and cook over moderate heat until crisp, 4 minutes. Add the celery and the remaining onion and garlic. Cover and cook over moderately low heat until softened, 7 minutes. Stir in the flour, then gradually whisk in the potato cooking water. Bring to a boil, whisking, and cook until thickened slightly. Add the potatoes and the cream and bring to a simmer. Add the salmon and monkfish and simmer over moderate heat, stirring a few times, until the fish is just cooked, 3 minutes. Add the mussels and clams and pour in their reserved cooking liquid, stopping before you reach the grit at the bottom; stir until heated through. Season with salt and pepper and add the parsley. Serve the chowder in bowls.