  We consider a model of multiband superconductivity, inspired by iron
pnictides, in which three bands are connected via repulsive pair-scattering
terms. Generically, three distinct superconducting states arise within such a
model. Two of them are straightforward generalizations of the two-gap order
parameter while the third one corresponds to a time-reversal symmetry breaking
order parameter, altogether absent within the two-band model. Potential
observation of such a genuinely frustrated state would be a particularly vivid
manifestation of the repulsive interactions being at the root of iron-based
high temperature superconductivity. We construct the phase diagram of this
model and discuss its relevance to the iron pnictides family of high
temperature superconductors. We also study the case of the Josephson coupling
between a two-band s' (or extended s-wave) superconductor and a single-gap
s-wave superconductor, and the associated phase diagram.
