Bottom Floor Toilet Overflow

[Canrun]

As of the weekend the bottom level toilet in my tri level house has begun to overflow. When I first moved into this 1960s tri-level in 2018 we had issues with roots and when there was a clog in the lines the bottom floor, floor drain would over flow onto the floor (concert basement style floor). For that problem we had a plumber come out and snaked the roots and fix the issue. Two years later I rented a auger from HD and cleared the lines and did not of any issues until now 4 years latter. Now we are having an issue where the bottom floor toilet is overflowing (on the same level as the floor drain). Seems like the issue happens when we run the dishwasher and take a shower in the same 3 hour window. Could the problem be the roots again ( I was thinking if it were the roots it would be over flowing on the floor drain) or could the problem be higher up maybe the dishwasher/ garbage disposal area or on one of the third level sinks/ toilets? Any advice would be greatly appreciated. (We have city sewage not septic)

 

[Canrun]

An update: Yesterday I rented a 75 ft. Drain Snake (rooter Jr.) and ran that down 75 feet about 8 times. After the first run of 75 feet I pulled a chunk of roots back. Switched attachments after the 2nd run and repeated this process 10 times.

After doing this I took a shower in my 3rd story bathroom to have the bottom level toilet overflow again. After this I did a process of elimination to see which items in the house where making the toilet over flow. After going through each shower and toilet and dishwasher I came to the conclusion the only thing that makes the bottom level toilet over flow is the 3rd level shower.

Any ideas on how to get this right?