Before designing any internal pages, you should consider how branding and navigational elements will appear consistently on all content pages.
Universal Branding: beyond the cover, you will need to find a way to apply simplified branding to all pages. Sometimes it is a smaller version of the masthead, sometimes only one letter or simplified version of the masthead or other graphic elements.
Universal Navigation: your content map should hopefully inform what is needed here. As the designer, you need to give the user the ability to jump to other content in the magazine directly from any page, rather than always going back to table of contents or swiping page to page. Did you determine that there were sections to your magazine in the content map? If so, the universal navigation needs to give the user the ability to jump to any section. Sometimes this navigation is a consistent nav bar, a pull out menu or a certain place on the page with navigational “buttons”.