Sharepoint for a small fraternal org. - is it possible?

You can have a few licensed users and use unlicensed guest accounts for the others. You can set up permissions for guests the same as licensed users: view only, read, contribute, edit, full control, and even site collection admin. Since you're only licensing a few, you may want to consider Business Premium to give yourself more security controls, but you can always start with Basic and see if you need more functionality. Here's a great start on guests in SharePoint https://learn.microsoft.com/en-us/microsoft-365/solutions/collaborate-in-site?view=o365-worldwide

Hope that helps!