Thoroughly combine strawberries, blueberries, raspberries, and blackberries in a bowl. Scoop out 3/4 cup of mixed berries and place into a saucepan with 1 cup water and sugar; set remaining berries aside. Bring the mixture to a boil and reduce heat to medium-low.
Whisk cornstarch and 1/4 cup water in a bowl until smooth and stir the cornstarch mixture into the hot fruit syrup; stir until the mixture thickens, about 2 minutes. Let the mixture cool completely, stirring occasionally, about 20 minutes.
Pour the thickened berry mixture into fresh berries until thoroughly combined; pour berries and sauce into shortbread pie crust. Place in refrigerator until chilled, at least 1 hour.
