Preheat oven to 350°. Pulse biscotti in a food processor until fine crumbs form (about 1-1/4 cups). Add butter; pulse until blended. Press onto bottom and up sides of a greased 9-in. pie plate. Bake until lightly browned, 8-10 minutes. Cool on a wire rack.
Beat 4 ounces cream cheese until creamy. Gradually beat in melted dark chocolate and coffee until blended. Fold in 3/4 cup whipped topping. Spread in crust. Freeze until set, about 30 minutes.
Beat remaining cream cheese until creamy. Gradually beat in melted milk chocolate until blended. Fold in 3/4 cup whipped topping. Spread over first layer. Freeze until set, about 30 minutes.
Place remaining whipped topping in a large bowl; fold in 1/4 cup caramel syrup. Spread over pie; top with shaved chocolate. Refrigerate until serving. If desired, drizzle with additional caramel syrup before serving.
