  We classify ground states and normal modes for $n$-component superconductors
with frustrated intercomponent Josephson couplings, focusing on $n = 4$. The
results should be relevant not only to multiband superconductors, but also to
Josephson-coupled multilayers and Josephson-junction arrays. It was recently
discussed that three-component superconductors can break time-reversal symmetry
as a consequence of phase frustration. We discuss how to classify frustrated
superconductors with an arbitrary number of components. Although already for
the four-component case there are a large number of different combinations of
phase-locking and phase-antilocking Josephson couplings, we establish that
there are a much smaller number of equivalence classes where properties of
frustrated multicomponent superconductors can be mapped to each other. This
classification is related to the graph-theoretical concept of Seidel switching.
Numerically, we calculate ground states, normal modes, and characteristic
length scales for the four-component case. We report conditions of appearance
of new accidental continuous ground-state degeneracies.
