Heat olive oil in a large skillet over medium heat. When the oil is hot, add the onions, chiles, garlic, olives, and taco seasoning. Sauté until the onions are soft and translucent.
Add the turkey, 2 cups enchilada sauce, and Greek yogurt to the skillet and stir gently until evenly combined. Simmer until the sauce begins to thicken, about 10-15 minutes.
Spoon some of the reserved enchilada sauce over the bottom of a 9x13 pan. Place 4 tortillas, overlapping, on the bottom of the pan.
Spoon ⅓ of the turkey mixture over the tortillas, then sprinkle with 1 cup of cheese.
Place another layer of tortillas over the cheese, followed by ⅓ of the turkey mixture and 1 cup of cheese. Repeat layers a third time, ending with cheese.
Bake at 375 for 30-40 minutes, until heated through and the cheese is bubbly.
Top with a dollop of Greek yogurt to serve. I would also put a wedge of lime on the plate because I love fresh lime juice on enchiladas.