  In this article, we prove twofold polynomial extension of Beigelb\"{o}ck's
\cite{b} multidimensional Central Sets Theorem (which was a common extension of
Furstenberg's Central Sets Theorem, and Milliken-Taylor theorem). We also find
the complete ultrafilter characterization of the multidimensional Central Sets
Theorems. Then we prove twofold common extension of Bergelson, Hindman, and
William's \cite{bhw} polynomial Milliken-Taylor theorem, and the
multidimensional polynomial Central Sets Theorems. We also find a sufficient
condition over two distinct multidimensional polynomials for which their
Milliken-Taylor image lie in the same color. This result gives a partial
polynomial extension of Deuber, Hindman, Leader, and Lefmann's \cite{d} result
on the separating Milliken-Taylor system.
