ASP.NET authentication is now a mature technology and sophisticated enough to meet all your requirements.
Moreover, there is even a better solution called ASP.NET Identity Server and comes with additional pairs:
- Can be used with Identity.
- Implements SSO (Single Sign-On)
- Can be used with Entity Framework.
- This is the host product itself.
So, to answer your questions:
No, you cannot use identification and simple membership.
Using ASP.NET Identity Server through a token.
You can customize the tables to suit your requirements.
Here is the official documentation for the identity server.
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