WordPress does not allow multiple registrations with the same email address, so while someone could use a different email address to register a new account, an existing user will not be able to "re-register" for another free account using an email address that matches their existing account.

how do I prevent people from creating multiple accounts with different email addresses?

One way would be to leave the default option here, where it requires that the end-user receive an email before they actually get their password. Of course, it's still possible to use me+this@ or another real email address variation, but it's a deterrent at least. I think that's really all you can do.