  We construct and explore the complex structures of boson stars, drawing
inspiration from similar configurations of non-topological solitons in
Minkowski space. These "molecular states" of boson stars have a multipolar
structure and both positive and negative Noether charges within one star, and
the opposite charges swap with time. Thanks to the gravitational attraction,
they exist even in the case of a free scalar field. We also explore the effects
of scalar self-interactions on these complex structures. We propose to use
galactic-scale charge-swapping boson stars as a potential solution to the
problem of the observed anisotropic distribution of satellite galaxies.
