The combination of prosciutto, plums, goat cheese, and arugula is seasonal, quick, and fresh.
Heat a grill until medium-hot. Generously brush one side of pizza dough with oil; grill, oiled side down, until underside is golden brown and top begins to bubble, 3 to 5 minutes. Quickly brush top with oil; flip crust. Top with some of the cheese, prosciutto, and plums. Grill until toppings are hot and crust is cooked through, 3 to 5 minutes more.
Slide pizza with a large spatula onto a cutting board. Drizzle arugula with oil in a large bowl, and toss. Drizzle pizza with oil; top with some of the arugula (or serve it on the side). Season with salt and pepper. Repeat to make more pizzas.