It very much depends upon how you want to affect the taste - in particular where in the brewing process that change has to happen. Changes in the grist, mash, boil affect the entire batch. Changes in fermentation depends upon how many fermentors the brewery has. Finally there is changes in packaging.
But even if your change could be delayed all the way until packaging time, it depends upon the brewer if they can and are willing to accommodate that.
I imagine you'd have more luck with smaller breweries. There is a 1200l microbrewery just down the road from me that uses disposable kegs - let's take them as an example. In principle they could add to their clearing tank some additional ingredients at the end of the kegging to add "something" to the beer for the last few kegs.
But even once you've got that far, you don't know how the mixture will turn out - balance is hard to achieve with just one shot.