Yes packages of shredded cheese can be frozen.
The best way to extend the shelf life of the shredded cheese is to put the packages of the shredded cheese into the freezer.
The freezer prevents the shredded cheese from going bad and growing mold on it.
The shredded cheese will last for a year or longer in the freezer and if you only refrigerate the shredded cheese it will last from 1 month to 3 months.
You can also shred up other types of cheeses as well and then place that shredded cheese in Ziploc bags or freezer safe containers and then the cheese will last for a year or more.
The texture of the cheese and the taste of the cheese may change when frozen but it still is good to eat.