I have a website with a certain divi theme already but I want to insert a new divi theme ( new pages ) without losing the old website. Can I add new pages with a different theme and make them private? Or even better can I create a new private project on the same website and preserve the old one till I’m done working on the new one.
No, you need to create a whole new, separate WordPress site. Most hosting will allow you to set up a subdomain and spin up a new WP instance.
Since it’s Divi, you can set up templates, and apply them to specific pages – while it doesn’t entirely function like you’re lookin for, technically it is possible.
You can enqueue unique style sheets, scripts etc, and dequeue the old on the new template pages.
But you really should pull a copy and build a new theme in staging, like u/bluesix recommended.