For the crusts: Preheat the oven to 350 degrees F. Unroll 3 of the pie crusts on a lightly floured work surface. Stack them on top of each other. Roll out the thick, layered dough to a 15-by-21-inch rectangle. Press into a rimmed baking sheet so that the crust comes up the sides and hangs over slightly. This will be the bottom crust. Chill until ready to use, at least 30 minutes.
Use the remaining crust for the top of the pie. Unroll it on a lightly floured work surface and roll it to a 14-by-18-inch rectangle. Cut the dough in half so you have two 7-by-9-inch pieces. One half will be the top crust for the apple portion of the pie. Cut the other half into 1-inch diagonal strips to use for the lattice on the cherry pie. Place the rectangle and strips on a parchment-lined baking sheet and chill until ready to use.
For the apple pie: Toss the apples in a medium bowl with the sugar and lemon juice. Melt the butter in a large skillet over medium-high heat, add the apples and cook, stirring occasionally, until tender, about 10 minutes. Stir in the flour, cinnamon and a pinch of salt and cook until thickened, about 1 minute more. Cool completely.
For the sour cherry pie: Place the cherries in a medium bowl. Whisk 1/4 cup cherry juice with the cornstarch in a small saucepan until completely smooth. Add the remaining cherry juice and sugar and bring to a boil over medium-high heat. Cook, whisking constantly, until thick and glossy, about 30 seconds. Pour the sauce over the cherries and gently fold to combine. Cool completely.
For the pumpkin pie: Whisk together the pumpkin, evaporated milk, sugar, pumpkin pie spice and the egg and in a medium bowl until smooth. Set aside.
For the pecan pie: Whisk together the brown sugar, corn syrup, butter, vanilla, eggs and a pinch of salt in a medium bowl until smooth. Fold in the pecans and set aside.
Once all fillings are made, begin assembling the pie. Remove both baking sheets with dough from the refrigerator.
Visualize the sheet pan is divided in half lengthwise and then crosswise so you have 4 equal quadrants. Each quadrant will hold a different pie filling. Prick the bottom crust all over with a fork.
Add the pie fillings in this order: Add the apple pie filling to the upper left quadrant of the crust; spread it to cover a 7-by-9-inch rectangle. Moving counter clockwise, pour the pumpkin filling right under the apple pie filling and spread it the same size as the apple filling. Spread out the cherry filling next to the pumpkin filling. Fill the top right empty space with the pecan filling.
Cover the apple pie quadrant with the reserved rectangle of dough. Lay the pie strips out diagonally over the cherry pie quadrant. Press any remaining strips of dough around the edge of the pie to thicken the rim. Crimp the edge of the pie, making sure to incorporate and crimp together the dough from the apple quadrant. Brush the edges and the dough on top of the pie with egg and sprinkle with turbinado sugar. Cut decorative slits in the apple pie crust.
Bake until all pies are set and the crust on the apple pie and cherry pie is golden brown and crisp, 55 minutes to 1 hour 5 minutes.
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