Bill Simpson, a meteorologist at the National Weather Service in Taunton, said Sunday that 6 to 10 inches are expected, and will likely be less.
He says Killingly in eastern Connecticut posted 3 inches on Sunday and about 4 inches of snow has fallen in Taunton.
The National Weather Service in Albany, N.Y., says snow is not expected to fall in upstate New York and the Berkshires. The forecast there is a 15 percent to 20 percent chance of passing snow showers.
Simpson said Boston also will largely be spared the brunt of the storm.
Southern New England was hit last weekend with a storm that dumped 2 to 3 feet of snow.