Generally, shredded cheese can last for several weeks after opening, if stored properly in the fridge. It's like keeping a good friend in the fridge, you want to make sure they're comfortable and happy, so they stick around for a while. This means keeping it in an airtight container, away from strong-smelling foods, and at a consistent refrigerator temperature.
If you're like me, you might have shredded cheese from different brands and types, like mozzarella, cheddar, or parmesan. The good news is that most types of shredded cheese have a similar shelf life, but it's always a good idea to check the packaging for any specific storage instructions. You don't want to be like me, and have to guilty-pleasure eat a whole block of expired cheese by yourself.