  Q-balls -- whether in the single-field or multi-field context -- are usually
studied in theories containing only one stabilising symmetry. However, this is
not the most general scenario. In this paper, we study a class of theories with
multiple symmetries. We consider both the traditional thin- and thick-wall
limits of these theories, deriving sufficient conditions for existence in the
latter case. Moreover, we also introduce a new state that could exist in this
class of theory -- a cored Q-ball. We show that this new state can be
energetically stable, but leave a detailed phenomenological study to later
work.
