Yes, the poles of a magnet can be changed by exposing the magnet to a very high magnetic field in a new direction. Many of the best magnets are sintered--densified from powder by heating at high temperature, often under pressure. If the magnet is a neodymium magnet, at room temperature you will need a strong pulse magnetizer to provide enough field. However, if you heat the magnet significantly, even a modest magnetic field can magnetize the magnet in a new direction.
Some sintered magnets are "anisotropic" with a strongly favored axis of magnetization. Such magnets can be reversed with a sufficiently high reverse field (or a modest reverse field at high temperature) but cannot easily be magnetized in directions transverse to the preferred axis.