  We address the system with two species of vector bosons in an optical
lattice. In addition to the the standard parameters characterizing such a
system, we are dealing here with the "degree of atomic nonidentity",
manifesting itself in the difference of tunneling amplitudes and on-site
Coulomb interactions. We obtain a cascade of quantum phase transitions
occurring with the increase in the degree of atomic nonidentity. In particular,
we show that the phase diagram for strongly distinct atoms is qualitatively
different from that for (nearly) identical atoms considered earlier. The
resulting phase diagrams evolve from the images similar to the "J. Mir\'o-like
paintings" to "K. Malewicz-like" ones.
