I know you have to write to someone higher up (I forgot who) and explain your situation and why you want an extension. If they approve it, you'll get another 2 weeks (I'm pretty sure it's 2 weeks).
I think you'll be okay time wise. You get 30 days to decide from the date on your acceptance letter. Say you were to ask for an extension and they give it to you, that's 6 weeks total.