Prepare each brownie mix according to package directions for chewy brownies in a 13- x 9-inch pan. Cool; break into large pieces.
Beat cream cheese at medium speed with an electric mixer until creamy; beat in marshmallow cream. Stir in 1 container of whipped topping; set mixture aside.
Stir together milk and white chocolate pudding mix, stirring until thickened. Stir in remaining container of whipped topping.
Crumble half of brownie pieces in an even layer in bottom of a 13- x 9-inch baking dish. Pour cream cheese mixture evenly over brownies; drizzle evenly with caramel topping. Pour pudding evenly over caramel topping; crumble remaining brownie pieces over top. Cover and chill 2 hours.
NOTE: For testing purposes only, we used Duncan Hines Chewy Fudge Brownie Mix and Smuckers Caramel Topping.