Leads submitting referrals

I have a customer that is organizing a referral program. Essentially, if you submit three referrals, then you are entered into a trip to Miami.

The problems are obvious - updating their own record - so what are peoples thoughts on the best way around this? Would it be to simply create some custom fields - referral #1 first name, referral #2 first name, etc - and simply map to those and then export that information? Is there a simpler way to do this?

Would love to hear anyones thoughts/ideas!