Some workplaces see people going above and beyond and reward that. Promotions come from operating at the level you want to be promoted to.
Some workplaces see it as a signal that they don't need a promotion because they can get the higher level work from you without the need to pay you more.
Know which one you're in before you decide how to approach it. If you've been there a while you should be able to figure out how things work. It's important to see how they actually work and not how you think they should work, otherwise you can end up doing a bunch of extra work for free.