Originally Posted by Saccharomyces
I stabilize and fine at the same time, on the third racking, and after it drops clear then I will rack again and pull samples to play with acid adjustments, tannin adjustments, etc. to taste. Once you decide what adjustments you want you can add about 2/3 of the amount you think you will need based on your glass experiments, taste again, etc. and once it's dialed in go to bottle.
Since I do all of my adjustments by taste only it would be impossible before the wine has been fined, since the yeast in suspension will affect the pH and drastically alters the taste and mouthfeel of the wine.
My process is a bit different, as I typically don't stabilize or fine until the very end, if at all. I only stabilize if sweetening, and I rarely sweeten. My wines tend to fall clear on their own, so I rarely fine.
I will do the acid and tannin adjustments in secondary, wait until another racking, adjust again if needed, etc. It's easy to add more if not enough (if the wine is "flabby" for example) but you can't take it out once it's in there. Sometimes oaking changes more than the tannins- it brings out any sweetness, too (from the vanilla notes) and so it doesn't need as much acid.