Besides the daily snowfall records, there are a couple other things that *could* come into play for Chicago if trends don't reverse.
The most snow to fall in a season from April 14 on is 6.9" in 1910. ORD currently has 5.4"
If Chicago were to receive at least 1", it appears that it would be the first time that 2 separate storm systems/complexes have produced 1"+ from April 14 on in the same season. Note that this is not the same thing as having multiple calendar days from April 14 on with 1"+ snow, which has happened in a couple instances when a storm spanned multiple days.