  Let $X$ be a homogeneous space of a real reductive Lie group $G$. It was
proved by T. Kobayashi and T. Oshima that the regular representation
$C^{\infty}(X)$ contains each irreducible representation of $G$ at most
finitely many times if a minimal parabolic subgroup $P$ of $G$ has an open
orbit in $X$, or equivalently, if the number of $P$-orbits on $X$ is finite. In
contrast to the minimal parabolic case, for a general parabolic subgroup $Q$ of
$G$, we find a new example that the regular representation $C^{\infty}(X)$
contains degenerate principal series representations induced from $Q$ with
infinite multiplicity even when the number of $Q$-orbits on $X$ is finite.
