I have a tub that just insist on being backed-up. I dont want to put another drop of drano in it for fear that the pipes will soon dissintergrate! When I treat it with drano i let it sit for about 12 to 18 hours and then plunge behind it with big pots of scolding hot water. This remedy's the problem for about 3 weeks, then the water is back up to my ankles in a matter of minutes when I take a shower, which is just nasty. We have the drain screens and try to make sure nothing goes in the drain.
Now what im sure got in the pipes was some of the glaze that started peeling not too long after we moved in the house 4 yrs ago.
Could be lack of vent causing the water to "Choke up" as it tries to exit the drain. Could be a cloged main drain. Could be "Back pitched" (Drain going uphill instead of downhill) could be hair and soap scum built up around the stopper.
You need to open a main dran clean-out plug and have the line inspected with video to see what is going on (roots? other clog? broken line? etc.),
Call a pro plumber or drain cleaning company with video equipment for an inspection and recommendation.
(Cease using caustic drain cleaner for your own safety. It obviously isn't solving your problem anyway.)