  Motivated by recent developments on visible actions on complex manifolds, we
raise a question whether or not the multiplication of three subgroups $L$, $G'$
and $H$ surjects a Lie group $G$ in the setting that $G/H$ carries a complex
structure and contains $G'/G' \cap H$ as a totally real submanifold.
  Particularly important cases are when $G/L$ and $G/H$ are generalized flag
varieties, and we classify pairs of Levi subgroups $(L, H)$ such that $L G' H =
G$, or equivalently, the real generalized flag variety $G'/H \cap G'$ meets
every $L$-orbit on the complex generalized flag variety $G/H$ in the setting
that $(G, G') = (U(n), O(n))$.
  For such pairs $(L, H)$, we introduce a \textit{herringbone stitch} method to
find a generalized Cartan decomposition for the double coset space $L
\backslash G/H$, for which there has been no general theory in the
non-symmetric case.
  Our geometric results provides a unified proof of various multiplicity-free
theorems in representation theory of general linear groups.
