Each state board has its own rules and sometimes laws regarding EPPP testing so you would need to review that for the new state. The state I was initially licensed in would approve you to take EPPP after they had all of your application information which included questions regarding other applications.
yes. you'd basically just be starting a new application to take it. It might be more cost-effective to just take it in your original state and pick a testing center in another state rather than applying for licensure in a whole other state depending on what you're trying to do.