We propose a realistic theory based on the SU(3)c⊗SU(3)L⊗SU(3)R⊗U(1)X gauge group which requires the number of families to match the number of colors. In the simplest realization neutrino masses arise from the canonical seesaw mechanism and their smallness correlates with the observed V-A nature of the weak force. Depending on the symmetry breaking path to the Standard Model one recovers either a left–right symmetric theory or one based on the SU(3)c⊗SU(3)L⊗U(1) symmetry as the “next” step towards new physics.
Reig, M., Valle, J. W. F., & Vaquera-Araujo, C. A. (2017). Unifying left–right symmetry and 331 electroweak theories. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 766, 35–40. https://doi.org/10.1016/j.physletb.2016.12.049