The only way to switch branches is to quit the job start the same career and this time select the other branch.
I have tried that, when after quitting, when selecting the job, there is no option to select branch. it always starts at the career level after selecting branch
What you have run into has always been the case with the game. You could never switch to the other branch in any career.
But, if you have Discover University, there is now a way to make it happen. And that is to go to University and get a degree that applies to the career you want to switch to. Once you graduate, you will get more choices and be able to access the careers you couldn't before. You will enter at level 7 or 8 too. You can select it directly too. You do have to make sure you are selecting the right one though as there will be a new separate entry in the career selection panel for the jobs your degree lets you enter.
Hope this helps
