Create a single website with 3 theme options in wordpress

Welcome to WordPress!

I think I understand what you are trying to do. I haven’t seen a plugin that will do this. Ideally, this is what WordPress does natively.

If you carefully pick the two themes that you want your user to be able to use, and then set up each one through the customizer, making sure to save your changes, then it should work.

The settings will be saved in the database.

If you choose your themes carefully, the website owner can switch between the themes without breaking anything.

When I set up a new site for a customer, I generally set up a few themes and then show them how to switch. Sadly, some widgets will be in the wrong location, occasionally the menu locations will need to be reset. But if you’ve got the main parts set up and the themes are compatible, you should be able to accomplish this.