  Let $M$ be an analytic complete finite volume pseudo-Riemannian manifold and
$\widetilde{Sp}(n,\mathbb{R})\times\widetilde{Sp}(1,\mathbb{R})$ a connected
semisimple Lie group such that its Lie algebra is
$\mathfrak{sp}(n,\mathbb{R})\oplus\mathfrak{sp}(1,\mathbb{R})$. We characterize
the structure of the manifold $M$ assuming that the Lie group
$\widetilde{Sp}(n,\mathbb{R})\times\widetilde{Sp}(1,\mathbb{R})$ acts
isometrically on $M$ and that its dimension satisfies
$3+n(2n+1)<\dim(M)\leq(n+1)(2n+3)$.
