Different Menu template for public and private pages.

I have a website that has public facing pages and subscriber only private pages. We want the private pages of our site to have different menu template (options) than the public facing main pages of our site. Is it possible to do this or would we need to create a whole new site for the membership pages? For instance, we have a public blog and a private (login access required) required and if we change the menu links for one it changes it for the other. Is there a way to segregate menu templates in enfold so the private area looks different than the main?

Any help would be much appreciated, thanks.