The PRIMitive Asteroid Spectroscopic Survey (PRIMASS) aims to characterize primitive asteroids throughout the asteroid belt in the visible and near-infrared (NIR). There are eight primitive families in the inner main belt: Polana-Eulalia, Erigone, Sulamitis, Clarissa, Chaldaea, Klio, Svea and Chimaera. PRIMASS has already characterized all 8 families in the visible, and the Polana-Eulalia complex in the NIR. Results of our previous work show that low inclination inner belt family asteroids fall into at least two distinct compositional groups: Polana-like (anhydrous and spectrally homogeneous) or Erigone-like (hydrated and spectrally diverse). In the visible, the Klio family is spectrally diverse and 23% of the objects show evidence of hydration, but it is not Erigone-like.We observed 21 objects in the Kilo family using the NASA InfraRed Telescope Facility (IRTF) and the Telescopio Nazionale Galileo (TNG) between January 2017 and March 2019. Our survey shows that the Klio family is spectrally homogeneous in the NIR, i.e., the heterogeneity seen in the visible does not extend to the NIR. The Klio family NIR spectra have mostly convex shapes and have red slopes (average slope 1.052 ± 0.425%/1000 Å normalized at 1.0 μm). The average spectra of both families we have studied in the NIR (Polana-Eulalia and Klio) differ slightly in spectral shape and slope, consistent with space weathering effects, but not conclusively so. Based on our NIR spectral comparisons, the Klio family cannot be ruled out as a possible source for two near-Earth asteroids: (101955) Bennu and (162173) Ryugu.