Bring blackberries, 1 1/3 cups sugar, and butter to a boil in a large saucepan over medium heat, stirring gently until butter is melted and sugar dissolves; remove blackberry mixture from heat.
Beat cream cheese and remaining 2/3 cup sugar at medium speed with an electric mixer until fluffy; add 2/3 cup milk, and beat until smooth. Stir in baking mix and uncooked oats. Spread two-thirds of the cream cheese mixture (about 3 cups) onto bottom of a lightly greased 13- x 9-inch baking dish; spoon blackberry mixture evenly over cream cheese mixture. Dollop remaining cream cheese mixture evenly over blackberry mixture.
Bake at 350° for 35 minutes or until golden brown.
Note: For testing purposes only, we used Bisquick All-Purpose Baking Mix.