Preheat oven to 475 degrees. In a bowl, toss escarole with radicchio, capers, red-pepper flakes, and oil.
Form dough (as directed in Basic Pizza Dough recipe) in a 9-by-13-inch rimmed baking sheet. Arrange cheese slices side-by-side to cover dough, then top evenly with escarole mixture. Bake until cooked through and crust is golden on edges and bottom, about 22 minutes.
Using a metal spatula, slide pie onto a cutting board. Scatter cherry tomatoes on top, squeezing each to release a bit of juice onto pie. Sprinkle with salt. Slice into 6 pieces and serve.