I agree with Nicole: multiple registrations in one form will go to a single record. It can not be done without aditional (custom) fields.
The email's "Forward to a Friend" could be a viable optiion, depending on the time the original lead is inviting friends.
If that is a "must have" on landing pages you will really need custom fields and, most important, Java, PHP or another server-side programming language. That requires a developer.
The logic is fairly simple and quick to implement: custom fields such as invitee1 and invitee2 are added to the form.
The form submits the data normally. The server-side language such as PHP reads $_POST and then calls SOAP API syncMultipleLeads to send the invitee1 along the standard form fields.
I did not try this and the logic may need fine tuning to work as intended. It will be close to my suggestion though. A good developer can figure this out very quickly.