Heat a large pot of salted water over high heat, bringing to the boil
Reduce heat to a simmer and add squid ink tagliatelle. Cook until al dente and drain, keeping ½ cup of the remaining pasta water.
In a separate pot, bring water to a boil. Reduce heat to a simmer and add mussels. Cook until mussels open, about 5 minutes. Remove from heat and drain.
While tagliatelle and mussels cook, heat oil in a skillet over medium-high heat. Add shrimp and crushed garlic. Cook until shrimp opaque, stirring frequently. About 2-3 minutes.
Add butter and heat until melted. Add white wine, lemon juice, reserved pasta water, kosher salt, and black pepper. Stir frequently and cook until reduced by half, about 10 minutes.
Stir in drained tagliatelle, cooking for 1-2 minutes
Remove from heat and serve immediately. Garnish with grated parmesan.