Yes you definitely can. If you sit for the exam under one state and you haven't applied for licensure yet, you can pay $25 with NASBA to transfer your scores and apply under a different state (https://nasbastore.org/ and click on “NASBA Candidate Score Transfer” under left-hand column).
This is my understanding. I have a non-reporting CPA license in MA which I'm not sure I'll be able to transfer, so I've done some research on my own. Someone correct if I'm wrong:
Once you're licensed and practicing in one state, under the new CPA mobility rules (https://www.cpamobility.org), as long as the license is active, unrestricted & in good standing, you may be able to work in many other states without filing or paying fees in that other state. Check cpamobility.org and put in the state you're licensed in and where you'll be working. But, as I understand it, if you want to set up a CPA firm in another state, you have to get licensed in that other state. To do that, you have two options – 1) apply for reciprocity CPA license in the 2nd state (this is fairly straight forward if the state you're already licensed in is recognized as substantially equivalent by NASBA – see https://www.nasba.org/licensure/substantialequivalency/) OR, if reciprocity is difficult/impossible you can 2) apply as a new CPA applicant in that state (will have to get a copy of your CPA score report again, send in all your transcripts again and verify experience again – all to make sure you're in compliance with that state's requirements).
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