Fifty-six crews have been working 72 hours straight since Friday.
By early Monday, all of Cleveland's main streets, about 300 road miles, were cleared, according to the city.
But 30 to 50 percent of neighborhood side streets were still impassable.
The city's own goal of clearing them by noon Monday was not met.
One big problem were the cars stranded or parked along the streets, getting in the way of the snowplows.
To add to that, even some of the snowplows themselves got stuck in the snow.
Cleveland's Chief Operations Officer Darnell Brown says the new goal is to have all streets passable by Monday's rush hour.
Stranded cars will be ticketed and towed.
And while Brown's sympathetic to owners of cars that are buried, he reminds them they should have moved their cars when the original parking ban was issued.