  In the standard quantum theory, one can measure precisely only a subset of
the incompatible observables. It results in lack of a formal joint probability
defining objective realism even if we accept nonlocal or certain
faster-than-light interactions. We propose a construction of such realism
extending the usual single-copy description to many copies, partially analogous
to familiar many worlds. Failure of the standard single copy can be easily
looked for experimentally. The copies should interact weakly at the macroscopic
level, leading to effective collapse to a single identical pointer state.
Experimental evidence for this conjecture could be obtained by detecting
incomplete collapse in sequential measurements or finding deviations from the
single-copy Born rule when observing simple quantum systems.
