Boil water for pasta.
Heat olive oil and some oil from anchovy fillets in a large pan. Finely chop the onion and fry until it softens. Add anchovy fillets and crushed garlic cloves and fry for a minute. Add canned anchovies and stir carefully. Lower the heat and let fish to heat through.
Cook the pasta. While it cooks, chop capers, half cherry tomatoes and add them to the pan. Tear half of basil leaves and add them to the pan with a handful of Parmesan. Mix everything until Parmesan melts, cover and turn off the heat. When the spaghetti is cooked, strain it and mix it with everything in the pan. Serve with more basil and Parmesan on top.