Using parchment paper, create a 5-inch-wide sling to fit along the bottom and up the short sides of the inside of the multicooker, leaving 3 inches of overhang on each side.
On a lightly floured surface, shape the pizza dough into an oval and fit it into the bottom of the pot on top of the parchment sling.
Cover with the lid, press Bake, and adjust the temperature to 370°F and the timer to 35 minutes. Bake for 15 minutes.
While the dough bakes, in a medium bowl, toss together the onion and grape tomatoes with the olive oil, salt, and black pepper. Let sit, tossing occasionally, until ready to use.
Using the overhangs, lift the sling, turn the dough over, and lower it back into the pot.
Spread the marinara sauce on top of the dough and sprinkle with 2 tablespoons of the Parmesan. Cover with the lid and bake until the bottom of the crust is golden brown and crisp, 12 minutes. Press Cancel.
Using the overhangs, transfer the pizza to a cutting board and sprinkle with the remaining 2 tablespoons Parmesean.
Toss the tomato mixture with the mozzarella and basil, and spoon over the pizza.