Toilets, Sinks, Showers, Tubs and Disposals - Clogged Whirlpool Tub

Hi, I live in a coop on the top floor (third floor) that was built in 1982. The master bathroom has a Whirlpool tub that we only use as a shower (due to us worried about germs from the previous owners). Occassionally, the tub will get clogged and we had used draino to get it unclogged. Recently when we use the Kitchen sink and the shower at the same time, the water will start to pool up in the tub. For the past week, draino and other commercial build up remover is not unclogging the Whirlpool tub. The sink and the toilet in the bathroom are ok and so is the connection for the washer and the main (full) bathroom.

I purchased a snake but we were unable to get very far into the pipe for the tub. I have tried to run the snake down the drain and opened up the lever (that open and stops up the drain) and nothing came out? Is there another area that I need to unclog in the tub? Is my clog in the kitchen too? I can't run the snake in the sink due to the grid down the drain.

Before I hire a professional, I want know whether my problem is on my floor or whether the problem is with the main sewer pipe.

Any help will be much appreciated!

Clogged Woes

Overflow is removed and snake run down through there. If you still have a problem after running the snake, then the problem could be caused where your line joins that of other unit(s). Has anyone else reported a problem in your units?