You can approach in a few ways. You can have the referral email address as the primary email address and the partner email as a secondary field that gets populated when they submit the form. Then the lead will have that information associated with it.
To sync this with salesforce you may need to use an API, not sure how you would do that part
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All is well until you want Marketo to recognize the revisiting partner for future form submissions. In order for the the form to pre-populate (using out-of-the-box functionality), the partner needs to be cookied on the landing page that's hosting the form. Since the unique identifier is email address, you would need the partner email address to be the primary one so that the all of the information from the partner's lead record can pre-fill the form.
What if you do this: if the number of partners is manageable, setup a partner portal/index page that has all of the partners on a single page. Clicking on each partner will take them to a partner page that could have all of their standard fields pre-populated (passing URL parameters from the portal page). This is assuming there is no highly sensitive/personal data visible for other partners to see. Just make sure you're using a landing page that has all tracking/cookie capabilities disabled.