Whisk together the sugar and cornstarch in a medium saucepan. Stir 3 ounces of raspberries, 3 ounces of blackberries, and 4 ounces of diced strawberries, and pour the lemon juice over the berries.

Place the saucepan over medium heat, stirring occasionally while the berries start to release their juice and break apart. Bring to a boil, then reduce the heat to a simmer. Cook the berries for 10 minutes, stirring occasionally to keep them from scorching on the bottom of the saucepan.

Once the compote is thick and the raspberries and blackberries have broken down, remove from the heat, and use an immersion blender (or carefully pour the compote into a blender) to smooth out the compote. This step is optional, but it works best if you want a smoother compote.

Pour the compote into a heat-proof bowl and let it rest at room temperature until cool.

Grease a 9 ½ inch baking dish with shortening or butter. Set aside.

Crush the graham crackers in a food processor, then pour in the melted butter while the processor is at low speed until the crumbs start to clump together.

Firmly press the crumbs into the bottom and up the sides of the greased pie dish. Place the crust in the freezer for 15-20 minutes or until it has hardened.

While the crust is in the freezer, pour the heavy whipping cream into a medium bowl and use an electric mixer to whip the cream until stiff. Set aside.

In a separate large bowl, add the cream cheese, sugar, sour cream, and vanilla, and use the electric mixer to mix until the cream cheese is smooth. Add the whipped cream, and mix at low speed until everything is combined and the mixture is fluffy and smooth.

Fold in the remaining 3 ounces of raspberries, blackberries, and 4 ounces of diced strawberries into the cooled compote and place it to the side.

Spoon the cream cheese mixture into the crust, and spread it out evenly. Then spoon the berry compote on top of the pie, cover it with plastic wrap, and chill in the fridge for at least 4 hours.

Serve chilled.