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