Preheat oven to 350 degrees F (175 degrees C).
Mash together the sweet potatoes and squash in a bowl. Fold the eggs, milk, cinnamon, nutmeg, and allspice into the potato mixture. Pour the mixture into the pie crust.
Bake the pie in the preheated oven for 30 minutes; arrange marshmallows on top of pie. Bake until a knife inserted into the center of the pie comes out clean, about 30 minutes more.