  Let $G$ be a connected complex semi-simple Lie group and ${\mathcal{B}}$ its
flag variety. For every positive integer $n$, we introduce a Poisson groupoid
over ${\mathcal{B}}^n$, called the $n$th total configuration Poisson groupoid
of flags of $G$, which contains a family of Poisson sub-groupoids whose total
spaces are generalized double Bruhat cells and bases generalized Schubert
cells. Certain symplectic leaves of these Poisson sub-groupoids are then shown
to be symplectic groupoids over generalized Schubert cells. We also give
explicit descriptions of symplectic leaves in three series of Poisson varieties
associated to $G$.
