Hi!

First off, with a plaster pool, a CH of 320 is well within the recommended range of 200 to 400ppm. So you're fine

pH and Total Alkalinity are linked. pH goes, up, TA goes up. pH goes down, TA goes down. If your pH is stable, I wouldn't worry too much about your TA. However, the BEST way to raise TA with minimal change in pH is to add ordinary Arm&Hammer or generic baking soda. That's all pool store Total Alkalinity Raiser is--baking soda. pH will probably go up, but when you lower the pH the TA won't go down as much. That's how you get around that link (there's a different, more complicated one to LOWER TA, but you don't need that).

If your chlorine tab is what most are, Tri-Chlor, then it's EXTREMELY acid and will lower your pH. Meanwhile, a new plaster pool as it cures will raise pH. So as long as your pH is between 7.2 and 7.8 I wouldn't adjust it.

Tri-chlor will also add CYA, aka Stabilizer. You need it to keep your chlorine for disappearing too fast but too much is also problematic. Check out our "Best Guess" table for optimal levels of Chlorine vs CYA.