A versatile approach for the synthesis of phased array (PA) antennas able to fit user-defined power pattern masks, while fulfilling additional geometrical and/or electrical constraints on the geometry of the array aperture and/or on the array excitations is presented. Such a synthesis method is based on the inverse source (IS) formulation and exploits the null-space of the radiation operator that causes the non-uniqueness of the IS problem at hand. More in detail, the unknown element excitations of the PA are expressed as the linear combination of a minimum-norm or radiating (RA) term and a suitable non-radiating (NR) component. The former, computed via the truncated singular value decomposition (SVD) of the array radiation operator, is devoted to generate a far-field power pattern that fulfills user-defined pattern masks. The other one belongs to the null-space of the radiation operator and allows one to fit additional geometrical and/or electrical constraints on the geometry of the array aperture and/or on the beam-forming network (BFN) when determined with a customized global optimization strategy. A set of numerical examples, concerned with various array arrangements and additional design targets, is reported to prove the effectiveness of the proposed approach.