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BEAT first 4 ingredients in large bowl with mixer until blended. Add whole eggs and egg whites, 1 at a time, mixing well after each. Gradually beat in 2 cups milk.
ARRANGE 9 bread slices on bottom of 13x9-inch baking dish sprayed with cooking spray; cover with half the berries and remaining bread slices. Pour Neufchatel mixture over bread. Let stand 30 min.
HEAT oven to 350°F. Bake French toast 40 min. or until golden brown. Meanwhile, bring remaining milk just to boil in saucepan; gradually add dry pudding mix, whisking 2 min. until blended. Remove from heat; let stand 5 min. Meanwhile, microwave remaining raspberries in small microwaveable bowl on HIGH 15 to 20 sec. or just until warmed.
SPOON pudding over individual servings of French toast; top with berries.