  We study multisymplectic structures taking values in vector bundles with
connections from the viewpoint of the Hamiltonian symmetry. We introduce the
notion of bundle-valued $n$-plectic structures and exhibit some properties of
them. In addition, we define bundle-valued homotopy momentum sections for
bundle-valued $n$-plectic manifolds with Lie algebroids to discuss momentum map
theories in both cases of quaternionic K\"{a}hler manifolds and
hyper-K\"{a}hler manifolds. Furthermore, we generalize the
Marsden-Weinstein-Meyer reduction theorem for symplectic manifolds and
construct two kinds of reductions of vector-valued 1-plectic manifolds.
