Pulse beefsteak tomatoes, garlic, red pepper flakes, and 2 tsp. salt in a food processor until smooth; transfer sauce to a large bowl and mix in cherry tomatoes, olives, capers, and 1/4 cup oil.
Cook spaghetti in a large pot of boiling salted water, stirring occasionally, until al dente. Drain pasta, reserving 1/4 cup pasta cooking liquid.
Add pasta, parsley, and butter to sauce. Toss vigorously with tongs, adding a splash of pasta cooking liquid or more as needed to create an emulsified sauce that coats pasta. Divide among bowls and drizzle with more oil.
