We carry a systematic study of possible extensions of the standard model based on the gauge group SU(3)_c X SU(4)_L X U(1)_X. We consider both models with particles with exotic electric charges and models which do not contain exotic electric charges neither in the gauge boson sector nor in the fermion sector. For the first case an infinite number of models can, in principle, be constructed, while the restriction to non-exotic electric charges only allows for eight different anomaly-free models. Four of them are three-family models in the sense that anomalies cancel by an interplay between the three families, and another two are one-family models where anomalies cancel family by family as in the standard model. The remaining two are two-family models.