Beat pudding mix and 1-3/4 cups milk in large bowl with whisk 2 min. Stir in COOL WHIP.
Layer about 1/3 of the grahams and half the COOL WHIP mixture in 13x9-inch pan, breaking grahams as necessary to fit; repeat layers. Top with remaining grahams.
Microwave chocolate and butter in medium microwaveable bowl on HIGH 1-1/2 min., stirring after 1 min. Stir until chocolate is completely melted and mixture is well blended. Add sugar and remaining milk; mix well. Spread over grahams.
Refrigerate 4 hours.