We propose a new strategy for robust high-quality self-assembly of non-trivial periodic structures out of patchy particles, and investigate it with Brownian Dynamics (BD) simulations. Its first element is the use of specific patch-patch and shell-shell interactions between the particles, that can be implemented through differential functionalization of patched and shell regions with specific DNA strands.The other key element of our approach is the use of layer-by-layer protocol that allows to avoid a formations of undesired random aggregates. As an example, we design and self-assemble "in silico" a version of a Double Diamond (DD) lattice in which four particle types are arranged into BCC crystal made of four FCC sublattices. The lattice can be further converted to Cubic Diamond (CD) by selective removal of the particles of certain types. Our results demonstrate that by combining the directionality, selectivity of interactions and the layer-by-layer protocol, a high quality robust self-assembly can be achieved. * oleksiyt@bnl.gov 2