  A constellation of $N=d-1$ Majorana stars represents an arbitrary pure
quantum state of dimension $d$ or a permutation-symmetric state of a system
consisting of $n$ qubits. We generalize the latter construction to represent in
a similar way an arbitrary symmetric pure state of $k$ subsystems with $d$
levels each. For $d\geq 3$, such states are equivalent, as far as rotations are
concerned, to a collection of various spin states, with definite relative
complex weights. Following Majorana's lead, we introduce a multiconstellation,
consisting of the Majorana constellations of the above spin states, augmented
by an auxiliary, "spectator" constellation, encoding the complex weights.
Examples of stellar representations of symmetric states of four qutrits, and
two spin-$3/2$ systems, are presented. We revisit the Hermite and Murnaghan
isomorphisms, which relate multipartite states of various spins, number of
parties, and even symmetries. We show how the tools introduced can be used to
analyze multipartite entanglement and to identify optimal quantum rotosensors,
i.e., pure states which are maximally sensitive to rotations around a specified
axis, or averaged over all axes.
