  We motivate and introduce a class of "hierarchical" quantum superposition
states of $N$ coupled quantum oscillators. Unlike other well-known multimode
photonic Schr\"{o}dinger cat states such as entangled coherent states, the
hierarchical superposition states are characterized as two-branch
superpositions of tensor products of single-mode Schr\"{o}dinger cat states. In
addition to analyzing the photon statistics and quasiprobability distributions
of prominent examples of these nonclassical states, we consider their
usefulness for high-precision quantum metrology of nonlinear optical
Hamiltonians and quantify their mode entanglement. We propose two methods for
generating hierarchical superpositions in $N=2$ coupled microwave cavities
which exploit currently existing quantum optical technology for generating
entanglement between spatially separated electromagnetic field modes.
