We study interaction of long internal breathers in the idealized conditions, which correspond to realistic summer density stratification in the western part of the Cyprus coastal waters near the offshore gas fields. According to the maps of nonlinear and kinematic parameters of internal waves, which have been produced in our earlier studies, in this region the coefficient of cubic nonlinearity in the Gardner equation is positive. Therefore, breathers of internal waves can be generated in such a medium, for example, during the degeneration of long disturbances (from tidal or atmospheric sources). A series of numerical experiments on the interaction of breathers in the framework of the Gardner equation was carried out. Statistical moments up to the fourth order were calculated, and spectral analysis of the interaction process was provided. The structure of the velocity field induced by internal breather as well as the corresponding loads upon underwater engineering constructions are determined.