I'm assuming that the 3" stack is carrying waste from another bathroom upstairs, right?
In KY, within the last few years they are now allowing what's called a "revent" which is a tee intersecting the stack that is sweeping upside down, opposite of what you would do for a vent.
This way the probability of clogging/wastewater/waste matter is not following back down the line into the vent serving the battery of fixtures.
The reason (in my opinion) they allow this now is the drastic increase of remodeling that has occured over the years where trailing a vent up through the walls of the existing home is extensive to accomplish the feat of a "code" worthy proper connection into the venting system.
This is for remodels only in most cases, no other time.
AAV's are mechanical, so they fail. Too often they are put in and forgotten. They don't, and won't ever provide the balance or equalization in a plumbing system to work effectively.
Like anything else, it needs clarification from your local plumbing inspector for the final say.