Possible future progress of the crystal-diffraction neutron electric dipole moment search experiment is discussed. A storage modification of the experiment is proposed. It is demonstrated that sensitivity of the method can be a few 10-27 e cm for the BSO crystal with the size 10×10×10 cm3 and expected luminosity of European Spallation Source (ESS). © 2010 Elsevier B.V. All rights reserved.