3 tablespoons olive oil
2 shallots, chopped
4 garlic cloves, crushed
Kosher salt, freshly ground pepper
2 oil-packed anchovy fillets, chopped
1 tablespoon tomato paste
28 oz. canned diced tomatoes, plus 8 oz tomato sauce
3 tablespoons chopped basil, or several pinches dried
¼ teaspoon red pepper flakes
½ cup clam juice
½ cup dry white wine
1 T butter
12 small clams, such as Manila or littleneck, scrubbed
16 mussels, scrubbed, debearded
10 ounces large shrimp, peeled, deveined
10 ounces bay scallops
12-16 ounces linguine
Heat oil in a large saucepan over medium. Cook shallots for a few minutes. Add garlic, stirring, until shallots are translucent, about 5 minutes more; season with salt and pepper. Add anchovies and tomato paste and cook, stirring, until color deepens, about 2 minutes.
Stir in tomatoes, tomato sauce, basil, red pepper flakes, and 2 tsp. salt. Bring to a boil, then reduce heat and simmer until sauce is thickened, about 15 minutes.
Add clam juice and wine and bring to a boil; cook 2 minutes. Lower heat and bring to a rapid simmer. Add clams and cook until they open, 8–10 minutes. Transfer clams to a large warm bowl; discard any that do not open.
Add mussels and cook until they open, approximately 5 minutes. Transfer mussels to bowl with clams; discard any that do not open.
Meanwhile, cook linguine in a large pot of boiling salted water until barely al dente, reserving 2 T. cooking liquid.
Return sauce to a boil, adding the reserved cooking liquid. Add shrimp and scallops, cover, cook one minute and remove from heat. Let sit until shrimp and scallops are cooked through, 5–8 minutes.
Transfer pasta mixture to a large bowl; season with salt and pepper. Arrange clams and mussels over pasta.