Adding Tannin to Finished Wine

Maybe someone will correct me but I do not see why not. You can add oak and that adds tannin. I would draw off a test batch and do it to it first though. You don't sound like you are real sure that is the problem. Did you test the acidity to see that it is not low?

Ray

You can add tannin to a finished wine. However, the tannin might cause precipitation of any positively-charged protein ions that are still in solution, and you may get some additional sediment. If you already used bentonite or other fining agents, this is less likely.

As Ray mentioned, oaking will add tannin, and a flavour that most people enjoy.

Tannin adds "astringency" to the wine, and helps it keep. Tannin is what gives the impression of "dryness" in the mouth after drinking. If there is too little tannin, the wine will be flat, insipid, and characterless. If there is too much it will be harsh, astringent, and bitter.

Strong tea will also add tannin to the wine, and will do so faster than oaking. I suggest you take some small samples, add various amounts of tea to the samples, and see if this is what your wine needs. If so, I suggest adding 12gms/gallon of medium toast french oak chips. Leave them in until the wine tastes just a bit more tannic than you like (as some of the oaking will dissipitate with aging).

You can put oak chips in some sort of nylon bag, so they can be removed later without racking. This will also fill the volume lost drawing your samples, so you needn't top up as much.