Light & Air Shaft Drain Backup

Anyone experience this? Also, when does the city become responsible for maintenance of drains? Our 8 unit building, which is self managed, has been recently having small flooding in our basement from the spillover/backup from the drain in our light and air shaft – only when there’s a strong thunderstorm, it seems. However, I’m afraid it’s only going to get worse as the storm season nears. We’ve cleaned out the drain ourselves near the surface however, it didn’t seem to resolve the problem. Any advice or recommendations for plumbers would be appreciated.