Hello there. When dealing with natural, additive-free cheeses, storage depends heavily on the moisture content of the variety you have purchased.
Hard cheeses like parmesan or aged cheddar can last anywhere from three to six weeks once opened if wrapped properly in parchment paper and stored in a breathable container. Semi-hard cheeses like swiss or gouda typically last for two to three weeks.
Soft, fresh cheeses such as mozzarella or ricotta have a much higher moisture content and should be consumed within three to five days of opening to ensure safety and quality.