The only way I did it without mods was finish one branch and then get him to quit. And then move this household to a totally new save and then get him the same job. It will reset to him having to start from Level 1 but at least you are able to go to the other branch when it's time to choose again. This is how I've always been doing it.
Alternatively, if you don't want to start a new save, I think you could also save the household after the sim has quit the job. Then just delete this household (or just keep them there first, just in case) and place the one you just saved from the Library to your current save. I haven't tried this method yet but maybe it might work. My guess is saving the household to the Library and putting them back in will reset the job progress.