The low-inclination (i < 8∘) primitive asteroid families in the inner main belt, that is, Polana-Eulalia, Erigone, Sulamitis, and Clarissa, are considered to be the most likely sources of near-Earth asteroids (101955) Bennu and (162173) Ryugu. These two primitive NEAs will be visited by NASA OSIRIS-REx and JAXA Hayabusa 2 missions, respectively, with the aim of collecting samples of material from their surfaces and returning them back to Earth. In this context, the PRIMitive Asteroid Spectroscopic Survey (PRIMASS) was born, with the main aim to characterize the possible origins of these NEAs and constrain their dynamical evolution. As part of the PRIMASS survey we have already studied the Polana and Erigone collisional families in previously published works. The main goal of the work presented here is to compositionally characterize the Sulamitis and Clarissa families using visible spectroscopy. We have observed 97 asteroids (64 from Sulamitis and 33 from Clarissa) with the OSIRIS instrument (0.5-0.9 μm) at the 10.4 m Gran Telescopio Canarias (GTC). We found that about 60% of the sampled asteroids from the Sulamitis family show signs of aqueous alteration on their surfaces. We also found that the majority of the Clarissa members present no signs of hydration. The results obtained here show similarities between Sulamitis-Erigone and Clarissa-Polana collisional families. The reduced spectra are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (http://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/610/A25