If i understand you well, you want to enable user two ways of verification process: 1) via custom logon window, and 2) via social media (whatever it means).
Creating custom authentication method is quite obvious. You can find tons of samples on Google. Second method is bit hard to implement, because those social media must provide a way to return information about result of verification process.
I do recommend to read this:
External Authentication Services with ASP.NET Web API (C#)[
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OWIN OAuth2 authentication via Social networks[
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You might be interested in
SSO (Single Sign On) method[
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Basics of Single Sign on (SSO)[
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Conclusion: No one can show you exact structure of database. It depends on many factors...