  In unconventional superconductors, understanding the form of the pairing
interaction is the primary goal. In this regard, Raman spectroscopy is a very
useful tool, as it identifies the ground state and also the subleading pairing
channels by probing collective modes. Here we propose a general theory for
multiband Raman response and identify new features in the spectrum that can
provide a robust test for a pairing theory. We identify multiple
Bardasis-Schrieffer type collective modes and connect the weights of these
modes to the sub-leading gap structures within a microscopic pairing theory.
The conclusions are completely general, and we apply our approach to interpret
the B1g Raman scattering in hole-doped BaFe2As2.
