The DAMA/LIBRA collaboration has recently published the final results of their phase 2 run. Combining this run with their prior two runs (DAMA/NaI and phase 1 runs, in total spanning ~ 16 years), they find an annual modulation amplitude A1 = 0.0102 0.0008 cpd/kg/keV (a 12.9 confidence level). There is significant tension between this result and that of other dark matter (DM) experiments, in particular those detectors based upon W and, more significantly, Xe. Employing the inelastic dark matter (iDM) scattering model of Smith and Weiner, a recent paper, based upon a proposed DM candidate mH (magnetic hydrogen), argues that this tension can be resolved in a certain region of the iDM parameter space. (The volume of this parameter space, afforded by uncertainties in cosmological parameters and the unknown masses of the constituents of mH, is actually quite large.) However, this solution (which would kinematically preclude all DM events in the W and Xe experiments) entails that the DAMA/LIBRA signal would be highly clipped (essentially no DM events in the winter), resulting in a rather large second harmonic amplitude. In this paper we further analyze the DAMA/LIBRA data (We derive our input data from their published figures.) in an effort to determine if the fit to the data is improved by including a second harmonic and what the amplitude of that harmonic might be. Combining all three of their data runs, we obtain an A1 in good agreement with their above noted published result (offering validation for our analytical approach) and find that there is some evidence for a non-zero second harmonic: A2 = 0.0011 0.0009 cpd/kg/keV (a confidence level of ~1.2 ). Implications of this result for A2 are discussed. Show Partial Abstract