Can you gift a Groupon to someone who has already purchased that exact Groupon?

So, basically my girlfriend purchased a Groupon for laser hair removal last month that will cover one area of her body. She's mentioned that she wishes she could have bought this particular package twice as there are two areas she'd like to use it on.

I looked at the ad and it says you can buy one for yourself, two for other people as gifts. I thought about buying a second package and gifting it to her for her birthday, but I want to be sure this will work and Groupon or the salon won't deny the gift transfer or something.

Anyone know?