Which Multiverse?

The complex (composite) systems such as the Universe allow the different decompositions into subsystems. The Everett's Many Times Interpretation (MWI) heavily relies on the occurrence of decohernce that should provide the classical reality for the Worlds. However, applying the occurrence of decoherence as the sufficient condition for the classical reality of the open systems, one seems obliged to consider the different decomposition equally (classically) realistic. But this leads to an inconsistency of the Everett's MWI in its very foundations: why the decomposition as we perceive it should be the only one realistic?