Context. Imaging exoplanetary systems is essential to characterizing exoplanet atmospheres and orbits as well as circumstellar disks and to studying planet-disk interactions to understand the planet formation processes. Imaging exoplanets or circumstellar disks in the visible and near-infrared is challenging, however, because these objects are very faint relative to their star, even though only fractions of an arcsecond away. Coronagraphic instruments have already allowed the imaging of a few exoplanets, but their performance is limited by wavefront aberrations. Adaptive optics systems partly compensate for the Earth’s atmosphere turbulence, but they cannot fully control the wavefront. Some of the starlight leaks through the coronagraph and forms speckles in the astrophysical image. Focal plane wavefront control, used as a second stage after the adaptive optics system, has been proposed to minimize the speckle intensity within an area called the dark hole. Aims. We previously demonstrated the on-sky performance of dark hole techniques, pairwise probing coupled with electric field conjugation, using the apodized pupil Lyot coronagraph of the VLT/SPHERE instrument. In this paper, we probe their performance using the SPHERE four-quadrant phase mask coronagraph, and we demonstrate the interest of combining dark hole techniques and reference differential imaging. Methods. We used these dark hole techniques on-sky to create a dark hole in the narrow band around 1.7 |j.m observing HR 4796. We then recorded broadband images of HR 4796 and a reference star at the H band. Results. The dark hole techniques improved the H-band detection limit by a factor of three. The dark hole was stable from one star to a nearby star enabling reference differential imaging. Conclusions. This stability offers two new strategies of observation. First, one can quickly create a dark hole observing a bright star before pointing to a faint target star. Furthermore, one can couple dark hole techniques and reference differential imaging. A very interesting point is that the performance of these methods does not depend on the astrophysical signal.