I have never had an issue at JFK, they seem to care more about the size of each bottle or whatever is under the 3 or 4 ounces or whatever the rule is then how many bags you are carrying. I've had two different quart zised bags because I was too lazy to combine/refill them, they never cared.

Put it in it's own bin as it goes through, they never know which bin goes to which person, you could bring seven of them on if you wanted to (another huge flaw in their practice, quart bag and shoes, quart bag and jacket, quart bag and carry on bag, quart bag and purse, all of a sudden I have 4 quart bags full of stuff and they never know)