Toilet backs up sometimes (perhaps partial clog?)

About a week ago someone in my house used liquid plumber on a perpetually clogged drain in our bathtub upstairs. It fixed the clog. A few days after that, someone flushed the upstairs toilet and suddenly the downstairs toilet started making a bubbling "glug glug" noise, air bubbles. I soon discovered the downstairs toilet was now clogged but the upstairs was all clear.

I plunged the downstairs toilet until it became unclogged and everything was fine. But about a day later someone flushed the toilet and all of the waste from the upstairs flush quickly backed up into the downstairs toilet and it began to overflow. I quickly unclogged the toilet and again, and again the line was free.

Now, every 1-2 days, the glugging sound returns and the downstairs toilet needs to immediately be "unclogged" or a single flush or shower will overflow the bottom toilet. I tried a snake and it either hit the blockage or the snake didn't hit anything, it's hard to tell, but it seems like this is some kind of partial clog in the drain that probably builds up solids like toilet paper or whatever over a period of a day or two and then becomes clogged again. It's the only thing I can think of. Perhaps the clog that was fixed in the upstairs shower broke loose and went further down the line?

All I know is that we're moving in a few months and I do not want to spend money on a plumber to fix this problem if I can fix it myself. I know it's not advised, but would trying liquid plumber in the downstairs toilet be good as a last resort? or perhaps even in the upstairs tub again to work its way down the drain?

Any thoughts on what this sounds like and how I can fix it? I realize it could be a venting issue but then it seems mighty suspiciously timed with the fixing of the other long-term clog in the tub. Considering I never had any problems like this with the downstairs toilet in a decade I'd be mighty surprised.

Thanks.

I would try the snake one more time, but make site is really getting in there use your hands to guide it with some gloves on if you have to. The issue might be in the actual sewer pipes also. They could be clogged causing the clogging to occur as the waste build up in your pipes in the basement. In order to get that fixes you'd have to call a plunger to wash out the pipes with high pressie water. I hope this helps

Never put liquid plumber in a toilet. Or any other drain cleaner directly in a toilet.