Be careful who you call about this because discharging into your sewer is typically not allowed (and perhaps considered stealing?). Usually your sewer rates are charged based on your water usage, so if you're putting more water to the sewer compared to how much water you are paying to come into your house, then you aren't actually paying for the processing of this additional ground water to get processed through the sewer system. I imagine any ethical plumber will disconnect your current setup and discharge to your yard. We ended up extending our discharge to the back of our property using PVC so that the discharge water doesn't go back into our sump.
If the city sewer line is full and not taking any more discharge from a storm, you could divert outside your premises although do so via a hose out to the alley. If you don't discharge far enough from the house it will just recirculate back to your sump. There is no issue with discharging into the city sewer system. It's perfectly code compliant. That's where everyone's sump, ejector or basin drains to.
Previous municipalities I've lived in have never allowed it because of the burden on the water process plant I'm interested in discharging to my sewer line if it's allowed, so if you could point me toward the Chicago code saying that we can do this I would appreciate it!
Our licensed architect designed our sump to discharge into the city sewer. The City of Chicago building department approved the design and issued a building permit. The city inspector then inspected the work and approved it. It's permitted,
I have a T switch installed which allows discharge into the city sewer and the other the the pvc pipe that runs out to the alley buried under my fence. The switch is turned to summer pipe via the outside pipe now and in the fall it's turned to the city sewer so the water isn't freezing in the outside pipe. Whatever works to keep your lower level dry...do it. Also don't forget to divert those gutter downspouts away from the house and not down into the pipe that runs underneath your home.