Use a large spoon to scoop 1 pint ice cream into thin, flat scoops, and then spread on bottom of crust. Smooth with back of spoon. Spread 1/2 cup caramel sauce over ice cream. Freeze pie until solid, 30 minutes to 2 hours.
Remove frozen pie from freezer and top with another 1/2 pint ice cream; spread evenly over caramel. Spread 1/2 cup fudge sauce over ice cream. Freeze pie until solid, 30 minutes to 2 hours. Remove frozen pie and top with final 1/2 pint ice cream. Drizzle remaining 2 Tbsp. each caramel and fudge sauce over pie. Freeze pie until solid, 30 minutes or up to 2 hours.
In a medium bowl, whip heavy cream and confectioners' sugar until firm peaks form. Transfer whipped cream to a plastic bag and snip off a 1/4-inch tip with scissors. Pipe whipped cream around edge of pie. Freeze until ready to serve. Serve with additional whipped cream, if desired.