3 is probably ok. I wouldn’t drink that much DAVKA to get the medical benefits. (Re Alzheimers: you can do a crossword or sudoku a few times a week also.) I don’t think that it’ll inevitably lead to more. If you’re getting nervous about addiction, try to make some fifty/fifty, regular – decaf.
If you have sugar with your coffee you may find you crash at different times during the day and need more coffee, leading to a vicious cycle. Try drinking it without sugar, or as much sugar. I’m leery of artificial sweeteners, though I just read that saccharin was taken off the carginogenic list a few years ago. Seems to be the least of the evils and may prevent your crashing.