Preheat oven to 350°F. Grease a 9 x 13-inch baking dish. Spread about ¼ cup of the enchilada sauce in the bottom of the pan; set aside.
In a large skillet, heat olive oil over medium-high heat. Add the onion and cook until softened, about 5 minutes. Add the garlic and cook, stirring constantly, until fragrant (about 30 seconds).
Remove from heat. Stir in chicken, ¾ cup of the enchilada sauce, ½ cup of the cheddar, ½ cup of the Monterey Jack, beans, corn, cumin, and chili powder. Taste and season with salt and pepper, if desired.
Place chicken mixture in the center of each tortilla.
Roll up and place seam-side down in the prepared baking dish.
Pour the remaining enchilada sauce over top. Sprinkle with remaining cheddar and Monterey Jack cheese.
Bake, uncovered, for about 20 minutes (or until the enchiladas are heated through and the edges of the tortillas are a bit crispy). Garnish with desired toppings and serve warm.