There’s nothing facebook-specific I’m aware of, but you can restrict who can sign up by their e-mail address domain, using the email domains whitelist site setting.
I currently use the whitelist to restrict the domain to a college domain. However according to some feedback people have provided, students would be more likely to sign up if they didn’t have to make another account. Hence the value of single sign on.
I’m trying to achieve easier onboarding while maintaining exclusivity to college community members.