Both career branches?

MCCC allows you to reset your career branch once you've picked one, so that you may pick the other branch. As far as I know, there's no way to do this without cheats or mods, and even some of those don't help (i.e. trying to demote sim with UI Cheats simply fires them, but keeps them on the chosen branch should they get their job back).

The game was designed to allow only one branch back in 2014 and never patched to allow both. MCCC is it.

Can I make one world and complete one branch of every career, then save my sim to the gallery, load them in a brand new world and complete the second branch? Then save the sim again?

Would that leave me with a sim that has all career objects unlocked?

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.

I had my sim quit when he was at the max of his career in one branch and went back and he was allowed to choose the other branch. Its possible to do

Are you sure? Whenever my sim quit their job it says they won’t be able to start over where they left off. ?