We report an optical spectroscopic study of SrMnSb2, a low-carrier-density metal. As temperature is decreased, our measurements reveal a large increase in the quasiparticle plasma frequency, which is highly unusual for a metal. This seemingly anomalous behavior can be accounted for using a "three-band" model of the multiband electronic structure of SrMnSb2 that includes two conduction bands and one valence band. The second conduction band is assumed to be heavy and its minimum is taken to be close to, but not intersecting, the Fermi level. At finite temperature, quasiparticles are thermally redistributed between the two conduction bands, leading to an increase in the optical effective mass and a decrease in the plasma frequency. The temperature dependence of the low-lying interband optical transitions and the Hall number can also be understood using our model. The phenomenology of such a three-band scenario has not been widely considered to date in optical spectroscopic studies. Our results provide an explanation for the puzzling optical properties that have previously been reported in a number of topical low-carrier-density metals and semimetals and lay a foundation for future optical studies of these materials.