  Let $G$ be a semisimple algebraic group whose decomposition into a product of
simple components does not contain simple groups of type $A$, and $P\subseteq
G$ be a parabolic subgroup. Extending the results of Popov [7], we enumerate
all triples $(G, P, n)$ such that (a) there exists an open $G$-orbit on the
multiple flag variety $G/P\times G/P\times\ldots\times G/P$ ($n$ factors), (b)
the number of $G$-orbits on the multiple flag variety is finite.
