Line 13×9 inch pan with foil, with ends of foil extending over sides of pan. Mix graham cracker crumbs and butter; press firmly onto bottom of prepared pan.
Refrigerate while preparing filling.
Beat cream cheese spread and sugar in large bowl with an electric mixer on medium speed until well blended. Smash drained berries with a fork; stir into cream cheese mixture. Gently stir in 2 cups of the whipped topping. Spoon over crust; cover.
Refrigerate 6 hours or overnight until firm. Use foil handles to remove cheesecake from pan before cutting into pieces to serve. Top with remaining 1 cup whipped topping. Store leftover gourmet cheesecake in the fridge.