Less than 3% of the known exoplanets were directly imaged for two main reasons. They are angularly very close to their parent star, which is several magnitudes brighter. Direct imaging of exoplanets thus requires a dedicated instrumentation with large telescopes and accurate wavefront control devices for high-angular resolution and coronagraphs for attenuating the stellar light. Coronagraphs are usually chromatic and they cannot perform high-contrast imaging over a wide spectral bandwidth. That chromaticity will be critical for future instruments. Enlarging the coronagraph spectral range is a challenge for future exoplanet imaging instruments on both space-based and ground-based telescopes. We propose the multi-stage four-quadrant phase mask that associates several monochromatic four-quadrant phase mask coronagraphs in series. Monochromatic device performance has already been demonstrated and the manufacturing procedures are well-under control since their development for previous instruments on VLT and JWST. The multi-stage implementation simplicity is thus appealing. We present the instrument principle and we describe the laboratory performance for large spectral bandwidths and for both pupil shapes for space- (off-axis telescope) and ground-based (E-ELT) telescopes. The multi-stage four-quadrant phase mask reduces the stellar flux over a wide spectral range (30%) and it is a very good candidate to be associated with a spectrometer for future exoplanet imaging instruments in ground- and space-based observatories.