Hi, John. To the best of my knowledge, there is nothing that an individual homeowner can do when the city sewers back-up into your basement with one exception. You can sue the city after the occurance. Your municipality probably has a Drain Commissioner or Water & Sewer Department that is responsible for this not happening. If enough homeowners sue and get enough money from the city, they suddenly decide to fix the sewers so that it doesn't happen again.
A long time ago, a buddy of mine took a basketball and jammed it into the cellar drain with a 2x4 when his started to back up. This worked but it could also cause the sewer pipe to crack. Thankfully, this did not happen but if it would have, he would have been responsible for replacing the sewer line on his property.
The best advise, I think, is for you to check with your municipality and see what they have done to fix the situation since 1987. If they have done nothing, you should start yelling.