At present, a variety of active and passive methods for generating microdroplets with different morphologies are available. Microcapsules with multi-core or compartment structures not only exhibit characteristics such as encapsulation, isolation, and leak prevention, but also possess specific functions, including enhanced buffering performance and superior heat transfer characteristics. Nevertheless, the high-throughput manufacturing of controllable multi-core droplets remains a significant challenge, constrained by the complexity of the equipment, the inconvenience of control, and the high cost. This study introduces a novel flow focusing method that integrates biphasic excitation to produce uniformly distributed double-emulsion droplets with a controlled number of cores at high throughput. The breakup of coaxial jets has been studied under different excitation frequencies, amplitudes, and flow rates of inner and outer liquids, with a particular focus on the change of the droplet morphology as the controllable parameter varies. By applying excitation to both the inner and outer jets in the weak coupling mode, our technique exhibits promising outcomes in achieving uniformity and controllability in the number of cores of the generated droplets. The scaling laws of the compound droplet size have been obtained, providing theoretical guidance for practical applications. The proposed biphasic excitation approach enhances the precision and efficiency of droplet generation processes in a range of applications, including pharmaceuticals, biotechnology, and materials science.