After you rack off the gross lees, you can add oak.
How much to add is a difficult question. How much wine do you have and how much oak flavoring do you want?
I add 1.5 to 2 oz cubes to 5 US gallons / 19 liters of red wine. For blackberry, I'd add half that, maybe less, as the wine is lighter in body and flavor. If you add 1/2 oz per 5 gallons, let it rest 6 to 8 weeks, then gently stir to homogenize, and taste. If you want more oak character, add more oak and repeat.