The only way I can think of, is if you don't export the finished puppet. Instead, when you build the puppet, make a copy of the Character Animator project folder and rename it something else (Puppet_01, Puppet_02). All those copies will then reference the orginal artwork. However, if you do any rigging changes, they will only be happen in the project you did those in.
If it's just the artwork you want to update (and not the rigging), you can export the puppet from the first project, import to the second project, then select the puppet in the project panel and look over at the properties. The first property is the path name to the artwork file it is using. When you import the puppet, this will point to a gathered media directory. But you can just edit the property and point it to the original file again.
But this will not share rigging between projects, only the artwork file. There is no good way to share rigging that i know of. But I often found I did not want to. My puppets drift over time, so I just keep the puppet with that project. I create different scenes using the same puppet a lot. Different scenes in one project allows you to share the puppet easily between the scenes. I then start new projects when i don't want to share things.