I once wished to transfer my state license to another state. I called the phone number of the EMS office in the other state (the one I wasn't licensed in) and had a nice chat with their staff. A very informative woman told me exactly what I needed to do in order to obtain a license in her state from her EMS office. I downloaded the forms she mentioned, filled them out, sent in a check, and a few months later I had a new card from that new state saying I could work on an ambulance there.
I continued to work in my original state on my original license and occasionally worked in the new state on the new license. I was licensed in two states to work on an ambulance. Each state had its own set of rules for how to maintain the license to work on an ambulance and when it came time to renew those licenses I made sure to do what each state individually wanted.
I don't know if any state requires you to give up all other licenses from all other states in order to work on their, but government is a strange thing with very strange rules. I urge you to call the state EMS office and have a conversation with them. One of the questions you should ask is if you are required to cancel all other state licenses. Their answer should be informative and helpful.
I love phones.