Is it possible to mature shop-bought hard cheese?
Yes you can mature cheeses, most hard cheeses can be matured either in the refridgerator or elsewhere.  Remove from the plastic packaging, the cheese will need to breathe, but not dry out - a cardboard box, paper towels, parchment paper would work.  Just be careful on the amount of moisture &amp; bacteria/mold growth.

You'll find a lot more helpful information if you search on "maturing cheeses" or "maturing cheeses at home".