Grant Inviter Role if Invitee Signs Up

I have a site that sells memberships using Ubercart 3 with a Membership product that assigns a role upon purchase.

What I'd like to do is promote the site by giving current users (members or not) 1 month of a free membership if someone they invite signs up. To sign up, they'd have to buy the Membership product, which would grant them the Member role.

It would work like this:

1. Person A invites Person B, C, and D.
2. If Person B, C, and/or D purchases the Membership, they are granted a Member role as usual.
3. If Person B, C, and/or D signs up, I want Person A to also be granted the Member role (or if they already have it, it would be extended 1 month for each of the people they invited that signed up).

Is this possible already? If not, I'd like to make this a feature request.