Well, I changed careers from an in-the-trenches mechanical design engineer to a publisher, trainer and consultant.
So, yes one can change engineering careers. However, once you get established in one discipline it can be challenging to change engineering disciplines.
I do know of one engineer whom has degrees in both electrical engineering and mechanical engineering – he works as a test engineer.
Moreover, I don’t think engineers have the career mobility many educational institutions claim. In general, you’ll take whatever opportunity is presented and likely stick with it.