We study a screening mechanism in the context of scalar -vector -tensor (SVT) theories. This screening mechanism is based on both the derivative self -interactions of the vector field and the interactions of the scalar field with the vector field and curvature. We calculate the field equations in a spherically symmetric space-time, and then, we study the conditions for which this mechanism is successful in a weak gravitational background. In order to corroborate these analytical results, we have performed a numerical integration of the full equations. Finally, the corrections to the gravitational potentials have also been computed. We conclude that the present model, including both kinds of interactions, can avoid the propagation of the additional longitudinal mode arising in these theories. We also show that the space parameter of the model is compatible with solar system constraints. This result extends the previous one found in the literature for generalized Proca theories to the case of SVT theories in the presence of scalar -vector interactions.