Preheat the oven to 350°. In a large skillet, melt 3 tbsp. butter over medium-high. Add the onions and celery; season with salt and pepper and cook, stirring often, until softened, about 10 minutes. Transfer to a large bowl. Reserve the skillet.
On a foil-lined baking sheet, arrange cornbread in a single layer and bake until browned in spots, about 15 minutes; let cool.
In the reserved skillet, heat the remaining 1 tbsp. butter. Add the sausage and cook, crumbling with a wooden spoon, until browned, about 5 minutes. Transfer to the bowl with the vegetables. Add the cornbread, cherries, chestnuts, apple and herbs; season. Drizzle with 1 cup stock and toss, adding more stock by the tablespoon if needed to just moisten the cornbread; season.
Transfer the stuffing to a 3-quart baking dish. Cover and bake 30 minutes. Uncover and continue baking until browned on top, about 15 minutes more.