  Excitations of ordered insulating magnets gain renewed interest due to their
potential topological properties and the natural realization of magnetic
analogues of the celebrated topological models. In this paper we go beyond
these parallels and explore what else is there in the unconventional
excitations of quantum magnets. We study the topologically nontrivial multiplet
excitations of the antiferromagnetic spin-1/2 kagome system with strong
breathing anisotropy and Dzyaloshinskii-Moriya interaction. We show that in the
chiral magnetic ground state the excitations can be characterized by a spin-1/2
doublet and a spin-3/2 quartet. With the use of magnetic field we can tune the
quartet through a band touching topological phase transition, when a novel
spin-3/2 Dirac cone is formed by the touching of four bands. In the
topologically nontrivial regime the spin-3/2 bands have large Chern numbers -3,
-1, 1, 3. In an open system the emerging chiral edge states naturally inherit
the multipolar characters and we find novel quadrupolar edge modes.
