  Let $G$ be the split orthogonal group of degree $2n$ over an arbitrary
infinite field $\mathbb{F}$ of chararcteristic not $2$. In this paper, we
classify multiple flag varieties $G/P_1\times\cdots\times G/P_k$ of finite
type. Here a multiple flag variety is said to be of finite type if it has a
finite number of $G$-orbits with respect to the diagonal action of $G$.
