Looks like loads more snow tomorrow, that's what Channel 2 Weather folks predict.

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A Lake Effect Snow Warning has been issued for Chautauqua and Cattaraugus counties from 1am Wednesday until 7am Thursday.Heavy lake effect snow is expected in the most persistent lake snows.
Grand total?
We could see 8-14" of snow in the affected areas.  Winds gusting up to 35MPH will produce blowing and drifting snow.
I hope you have a neighbor with a snowblower!