You can have another identical tree which can have its own password but I think you will find that it can only be done by adding another site with a different site title and different ID.
Click on your "my account" and you will see "create a new web site".
Also when in edit mode, go to help/tutorials and read the security part about passwords. You can set this up so that members you invite can create their own password. Alternatively you can set the password for the site.