Place blackberries (or peaches or cherries), 1 1/3 cups sugar and butter in a large saucepan and bring to a boil. Stir gently until butter is melted and sugar has been dissolved. Remove mixture from the heat.
Beat cream cheese and remaining sugar at medium speed with a mixer until fluffy. Add 2/3 cup milk and beat until smooth. Stir in baking mix and uncooked oats by hand. Spread two-thirds of the cream cheese mixture onto the bottom of a lightly greased 13 x 9 baking dish. Spoon blackberry mixture evenly over the top of the cream cheese mixture. Dollop remaining cream cheese mixture evenly over the blackberry mixture.
Bake at 350° for 35 minutes or until golden brown.