If there are viable yeast cells (probable) and you add sugar
(well-dissolved) to the wine, chances are it will easily re-ferment. The
only trouble you might have is if the alcohol percentage is already near the
threshold of the chosen yeast strain's tolerance. I would remove a portion
of the liquid, dissolve the sugar in it, and add it back to the wine. You
should be able to estimate the quantity to add using the various sugar/SG
tables on the internet.

Regarding the 11.5-12% target PA to balance blackberry, I would say that is
highly dependent on the fruit quantity used in your must. I recently
fermented a 15% blackberry wine (by accident...) but I used 100% juice- no
water - and it is not unbalanced at all. I did nonetheless dilute it by 10%
following fermentation to attain 13.5% alcohol and balance the acid (THAT
was the issue, not the alcohol).

Roger
Quinta do Placer