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Arrays of volumetric antennas whose minimum spheres overlap are efficiently analyzed by means of translational addition theorems for spherical modes in this letter. For this purpose, an improved model of the isolated antenna in terms of elementary sources of infinitesimal dipoles is used. The model provides a generalized scattering matrix (GSM) in terms of infinitesimal dipoles that allows synthesizing the whole behavior of the isolated antenna and enables its precise application to array environments by using translational addition theorems. The search region for the optimization procedure that finds the positions of the elementary sources to model the isolated antenna has been extended to the volume occupied by the antenna, so that the model becomes very precise. As a consequence, even when the minimum spheres of the array elements are strongly overlapped, it provides accurate results since the equivalent models will never overlap. Additionally, the optimization procedure is carried out only once for a wide band. The proposed approach has been validated by means of two different radiating elements such as monopoles and dielectric resonator antennas (DRAs), with good agreements obtained in comparison to the full-wave results simulated by commercial software.