Multiple volume reflections of the 400 GeV / c proton beam by the sequence of fourteen bent silicon strips has been studied at the CERN SPS. The sequence is close to be parallel that is the spread of the strip orientation angles is much smaller than their bend angle and eleven strips working coherently in the regime of volume reflections deflected the beam by 110 μrad with the efficiency 88%, which is significantly larger than the estimation based on independent reflections. The mechanism giving the efficiency increase has been studied by simulation. It appears that many particles volume captured in one of the strips take part in volume reflections in the subsequent ones. Such a crystal multi reflector can be successfully used as a primary collimator for the beam halo collimation of high-energy accelerators.