Preheat the oven to 350°F (175°C).
In a large mixing bowl, combine the shredded cooked chicken, diced ham, shredded Swiss cheese, and cooked pasta.
In a separate bowl, whisk together the condensed cream of mushroom soup, sour cream, mayonnaise, Dijon mustard, garlic powder, onion powder, and black pepper until smooth.
Pour the sauce mixture over the chicken, ham, cheese, and pasta mixture. Stir gently until all ingredients are evenly coated.
Transfer the mixture to a greased 9×13-inch casserole dish and spread evenly.
In a small bowl, mix the crushed buttery crackers with the melted butter until the crumbs are evenly coated.
Sprinkle the buttery cracker topping evenly over the casserole.
Cover the casserole with aluminum foil and bake for 30 minutes.
Remove the foil and bake for an additional 15 minutes, or until the topping is golden brown and the casserole is heated through.
Remove from the oven and let it cool for 5 minutes before serving.