  The paper outlines a new development in the Contextuality-by-Default theory
as applied to finite systems of binary random variables. The logic and
principles of the original theory remain unchanged, but the definition of
contextuality of a system of random variables is now based on multimaximal
rather than maximal couplings of the variables that measure the same property
in different contexts: a system is considered noncontextual if these
multimaximal couplings are compatible with the distributions of the random
variables sharing contexts. A multimaximal coupling is one that is a maximal
coupling of any subset (equivalently, of any pair) of the random variables
being coupled. Arguments are presented for why this modified theory is a
superior generalization of the traditional understanding of contextuality in
quantum mechanics. The modified theory coincides with the previous version in
the important case of cyclic systems, which include the systems whose
contextuality was most intensively studied in quantum physics and behavioral
sciences.
