Make the crust: In a large bowl, combine the flour, sugar, and salt. Add the butter and shortening; using a pastry cutter, cut the fat into the flour mixture until it resembles coarse sand. Alternatively you can use a food processor fitted with a metal chopping blade, pulsing until the fat is cut in. Transfer to a mixing bowl.
Drizzle about half of the water over the flour mixture; using a fork, gently work the mixture into clumps to begin to form a dough. Drizzle the remaining water and continue working just until the dough comes together. Use your hands to pull in the last bits of flour, being careful not to overwork and melt the butter. Shape the dough into a ball.
On a clean surface, flatten the dough to a 1⁄2-inch-thick disk, then fold it over itself. Flatten and fold 4 additional times to form layers. Divide the dough into 2 equal pieces, about 15 ounces each. Shape each half into a disk, wrap them each in plastic, and refrigerate 6 hours or overnight. Pull the dough from the refrigerator 15–20 minutes before you are ready to roll it out.
Make the filling: Combine the plum slices, berries, sugar, vanilla, and salt in a large bowl and let stand for 30 minutes. Strain off the juices, sprinkle the fruit with cornstarch, and mix well to dissolve the starch.
Assemble the pie: Meanwhile, preheat your oven to 400°F. Grease an 8-inch metal pie plate with butter. Dust your countertop with flour and roll one half of the pie dough into a 15-inch circle. Gently lift the crust and settle it into the pie plate, leaving any overhanging crust intact. Pour the fruit mixture into the crust and press it down carefully to fill.
Roll the second half of the crust into a 6-by-14 inch rectangle. Use a knife or a fluted pastry cutter to cut the rectangle into 1⁄2-inch strips. Place one strip across the center of the top of the pie. Leaving an equal amount of space between each strip, lay one strip on either side of, and parallel to, the first. Working in the opposite direction, weave the remaining strips of dough perpendicularly over and under to create a lattice. Trim the ends of the lattice strips to the same size as the bottom crust, then fold the bottom layer up and over the loose strips. Crimp the edges between two fingers and your thumb to decorate the rim of the pie. Chill the pie in the freezer for 15 minutes or till the dough is firm like cold butter.
Bake in the preheated oven for 20 minutes, then lower the temperature to 350°F until the juices are thickened and bubbly and the crust is evenly golden, 1 hour and 10–20 minutes. If the outside edge begins to darken before the rest of the pie is finished, loosely cover the rim with aluminum foil for the remaining time. Let the pie cool completely, about 2 hours, before serving.