Preheat oven to 375°. Heat oil in a large frying pan over medium heat. Add onion and cook until translucent, about 4 minutes. Add spinach and cook, stirring as needed, until almost completely wilted. Add corn and cook until hot. Set aside.
Put 6 ovenproof baking dishes* (each about 12-oz. capacity) on a rimmed baking sheet. Working with one dish at a time, spoon in 2 tbsp. enchilada sauce. Top with 2 tortilla quarters, 2 rounded tbsp. each refried beans and black beans, 1 tbsp. cheese, and 2 more tortilla quarters, pushing tortillas down gently as you layer them over cheese and beans. Spoon in 1/3 cup (packed) vegetable mixture, then 2 more tortilla quarters, 3 tbsp. enchilada sauce, and 2 tbsp. cheese. Repeat layering with remaining dishes.
Bake enchiladas until bubbling, cheese is melted, and tortillas are starting to brown on edges, about 30 minutes. Sprinkle with green onions.
*Or use a 9- by 13-in. baking dish, spreading one-third of sauce over bottom; top with one-third of tortillas, the beans, one-third of cheese, one-third of tortillas, the vegetable mixture, remaining tortillas, remaining sauce, and remaining cheese.
Note: Nutritional analysis is per 1 1/2-cup serving.