Temperature dependent high resolution photoemission spectra of quasi-one-dimensional Li(0.9)Mo(6)O(17)evince a strong renormalization of its Luttinger-liquid density-of-states anomalous exponent. We trace this new effect to interacting charge neutral critical modes that emerge naturally from the two-band nature of the material. Li(0.9)Mo(6)O(17) is shown thereby to be a paradigm material that is capable of revealing new Luttinger physics.