Mix sugar, pumpkin pie spice and corn starch in a large bowl.
Cut apples into 1/4-inch thick slices and place in a separate bowl.
Sprinkle apples with lemon juice and rum; add to dry ingredients. Stir to combine.
Place in piecrust. Dot with 2 tablespoons of butter.
Drizzle with caramel sauce.
Stir flour and brown sugar together in small bowl.
Cut in 1/4 cup butter until mixture resembles coarse meal.
Sprinkle evenly over top of pie.
Bake in a preheated 400 degrees F oven for 10 minutes. Reduce heat to 350 degrees F and bake an additional 40 to 50 minutes, until golden brown. Delicious when served warm with a scoop of vanilla ice cream.