It makes sense. I have never heard of it, and I think the problem would be keeping proficient in your skills. That being said, I know in Washington, you can only work to the level your agency will sponsor you to. For example, I am an I-85 (Ok....well now with name changes I am a WA State Advanced EMT....but whatever). But until things changed about a year ago, my fire department would only sponsor me up to EMT-B. Even though I work on the ambulance as an EMT-I, when working for the FD, I had to work as a basic.