How can I make a shared album a private album

There is complete mismatch between the title and body of your post.

Shared albums are meant for those who you invite to view, that's it. It remains private to the extent of people whom you have invited --> If Shared Albums aren't working - Apple Support

You can add photo to any album. Keeping adding any photo to multiple albums.

Open an album > tap Select > Tap a photos or multiple photos > tap "Add to" at the bottom > Select Album to add to.