You can try to join with another email address, but it might or might not work. My wife account worked, while my co-worker did not.
Key is whether they see you as already a member. Clearly, the same email address is a unique identifier and you won't be eligible for the referral promo if yours is already in their database. Name alone won't prevent it, as many people have the same name. Same with address or phone number... sometimes different people share the same residential info. A combo of name and phone number and/or physcial address, however, might trigger a duplicate identification. Bottom line is that if you're rejected and you're willing to orphan your old account and get a new one with the referral, change as much info as possible (at minimum, email address) as you can while still keeping it legit. Using your work or vacation home addy, secondary phone number, etc. could help. Don't plan on signing up anew and then asking to merge with your old account. While you *might* be able to get away with it, if seen as a purposeful duplicate with the intent to run up points, they might decide to wipe you out.