Bring potatoes, onions, and 6 cups of the fish stock to a gentle simmer in a large saucepan over medium heat. Cover and cook until potatoes and onions are tender.
Meanwhile, toast saffron in a small skillet for 1 minute over high heat. Remove from heat and crumble threads with your fingers into simmering potatoes and onions.
Heat 1 cup of the remaining fish stock in a large saute pan, add clams, cover, and cook over medium-high heat for about 5 minutes. Add mussels, cover, and cook until all the shells open. (Discard any that don't.) Remove from heat; transfer clams and mussels to a large serving bowl. Strain poaching stock to remove any grit, and add to potatoes and onions.
In the same saute pan, bring the last remaining cup of stock to a simmer over medium heat. Cut cod into pieces, about the same size as scallops. Add cod and scallops to the simmering stock and poach for 5 minutes. Transfer seafood to the serving bowl and set aside. Add stock to potatoes and onions.
Use a slotted spoon to strain most of the potatoes and onions from the stock and scatter over seafood. Leave about 1⁄2 cup potatoes in stock. Mash to slightly thicken stock, or puree in a food processor and return to pan, then raise heat, add cream, and boil for 5 minutes to reduce and thicken slightly. Season to taste with salt and pepper. Pour stock mixture into serving bowl over the seafood. Serve garnished with parsley and chives.