What kinds of rocks can undergo metamorphism?
Metamorphism is a broad term for the processes that change one rock into another rock. The new rock is called metamorphic - one of the three major rock types. The other main rock types are igneous and sedimentary.
When it comes to metamorphism, the original rock type is not very relevant because any rock can undergo metamorphism if it is buried deep enough and/or heated. When the temperature and pressure acting on a rock change, its constituent minerals change to become more chemically stable.
For instance, subjecting basalt (an igneous rock) to extremely high pressure and moderate temperature can convert it to eclogite, which is a metamorphic rock. This occurs because the minerals inside basalt are converted into different minerals that are more stable under extreme conditions. However, the eclogite can still undergo metamorphism. This actually happens when a body of eclogite is uplifted and the pressure upon it decreases, converting it into a new rock called granulite.