Specular reflection is one of the most fundamental processes of optics. At moderate light intensities generated by conventional light sources this process is well understood. But at those capable of being produced by modern ultrahigh-intensity lasers, many new and potentially useful phenomena arise. When a pulse from such a laser hits an optically polished surface, it generates a dense plasma that itself acts as a mirror, known as a plasma mirror (PM). PMs do not just reflect the remainder of the incident beam, but can act as active optical elements. Using a set of three consecutive PMs in different regimes, we significantly improve the temporal contrast of femtosecond pulses, and demonstrate that high-order harmonics of the laser frequency can be generated through two distinct mechanisms. A better understanding of these processes should aid the development of laser-driven attosecond sources for use in fields from materials science to molecular biology.