They'll probably check billing methods as well, so you'd have to generate a lot of extra credit cards accounts. And they could ensure that the #'s for these can only be used once by one amazon account or shipping address.
Yeah, I wouldn't be surprised if Amazon restricts your account to one of these gift certificates somehow. The deal description said "no gifting allowed."
Still, a separate e-mail address, credit card, and Amazon account would be an almost surefire way to get a multiple deals. But anything past 2 or 3 would get to the point of just wasting your time.
Some credit cards allow you to generate throwaway credit card numbers, and you could sell the gift certificates to people with different addresses.
My main reaction to this story is that, after months of getting crappy offers from LivingSocial and cancelling my subscription to them, they finally offer something good.
That way if/when they invalidate all of the orders from people who ordered more than 1, you won't miss out on the deal.