The PRIMitive Asteroid Spectroscopic Survey (PRIMASS) is a visible and near-infrared study of primitive asteroids throughout the asteroid belt. Nesvorny et al. 2015 defined 6 primitive families in the inner asteroid belt: Polana-Eulalia, Erigone, Sulamitis, Clarissa, Chaldaea, and Klio. PRIMASS has already characterized Polana in visible and NIR, and Erigone, Sulamitis, and Clarissa in the visible (de Leon et al. 2016; Pinilla-Alsonso et al. 2016; Morate et al. 2016, 2018). Our published results show that inner-belt primitive asteroids fall into at least two distinct compositional groups: Polana-like (spectrally homogenous and no 0.7-micron absorption) or Erigone-like (hydrated and spectrally diverse). Objects in the Sulamitis family are Erigone-like in the visible (Morate et al. 2018). No work has been published on the Klio family in the visible, but there are multiple published spectra of the parent body (84) Klio. In this work, we present near-infrared spectra of 15 objects in the Kilo family and 5 objects in the Sulamitis family, obtained with NASA's InfraRed Telescope Facility (IRTF) and the Telescopio Nazionale Galileo (TNG) between August 2017 and June 2018. Our initial results show clear differences between the Klio and Sulamitis families in the NIR, evident even in a small sample size. Within the uncertainties, Kilo objects are identical to each other and show essentially flat spectra with no slope and no features. In contrast, Sulamitis objects are more spectrally diverse which agrees with what is seen in the visible. Asteroid (84) Kilo shows a clear 0.7-micron feature, associated with hydrated material (Fornasier et al. 2014), which suggests that there is a third compositional group of inner belt families that are Klio-like (hydrated and spectrally homogeneous). These three spectral groups occur at three different inclinations: Polana-like are at low inclination (i<3°), Erigone-like are at mid inclination (3°8°); i.e., there are similar compositions among three groups with distinct inclinations.