In a large saute pan over medium-high heat, add 1 tablespoon of the olive oil and the shrimp. Sear on both sides, 1 to 2 minutes per side. Set the shrimp aside on a plate (they will be cooked more later) and reserve the pan.
Bring a large pot of salted water to a boil. Add the spaghetti and cook until just shy of al dente according to the package directions. Before draining, reserve about 1/2 cup of the cooking water.
Meanwhile, add the remaining 1/4 cup olive oil to the saute pan over medium heat. Add the crushed red pepper and garlic and cook until the garlic edges are just slightly brown, 3 to 4 minutes. Add the tomatoes and lightly smash them with the back of a spoon to release their juices. Cook, stirring often, until thickened slightly, 3 to 4 minutes. Add the mussels, cover and cook until they open and release their juices, 4 to 5 minutes.
Raise the heat to medium high and add the shrimp back to the pan. Add the spaghetti and a little of the reserved pasta water and cook, tossing and adding more pasta water as necessary to keep the pasta moist, until the shrimp begin to turn pink, about 2 minutes. Add the parsley and basil and season with additional salt if needed. Transfer the spaghetti to warm bowls.