Put the strawberries, blackberries, blueberries, and juice in a medium pot over medium-high heat and cook, stirring constantly, for 4–5 minutes.
Add the raspberries and cook for 1 minute longer.
Using a slotted spoon, fish out the berries into a medium bowl and set them aside.
Cook the remaining juice in the pot over medium-low heat, stirring occasionally, until thick and syrupy, about 10 minutes. As more of the berry liquid evaporates, gradually decrease the heat. The thicker the syrup, the better.
Remove the syrup from the heat. Add the reserved berries and stir to combine.
Let cool slightly before serving. May also be served chilled or at room temperature.