Bring a large pot of salted water to boil. Cook pasta according to package directions for al dente. Drain pasta and set aside, reserving 1 cup of pasta cooking water.

While pasta is boiling, melt 2 tablespoons of the butter in a large skillet over medium-high. Add shallot, garlic, capers, and anchovies. Cook, stirring often, until shallot and garlic are softened and starting to brown, and anchovies are disintegrated, 1 to 2 minutes. Add crushed red pepper, cook, sitting constantly, until fragrant, about 30 seconds. Add tomatoes and 2 tablespoons of the butter; cook, stirring occasionally, until starting to soften, about 2 minutes. Add ½ cup of the reserved pasta cooking water and bring to a simmer over medium-high. Reduce heat to medium and simmer, stirring occasionally, until tomatoes burst and sauce has thickened, about 5 minutes.

Reduce heat to medium-low and stir in lemon zest, lemon juice, mackerel, and mussels. Cook, gently stirring occasionally, until heated through, about 1 minute. Add drained pasta, parmigiano, ¼ cup of the pasta cooking water, and the remaining 2 tablespoons butter. Cook, gently tossing, until pasta is evenly coated in sauce, adding remaining reserved pasta cooking water as needed to loosen sauce. Remove from heat and stir in parsley.

Divide between 4 bowls, garnish with additional parmigiano and parsley, and serve immediately.