In microfluidic step emulsification, the size of droplets generated in the dripping regime is predominantly determined by the nozzle's height and only weakly depends on the applied flow rates or liquid properties. While the generation of monodisperse emulsions at high throughput using step emulsifiers has been well established, the generation of double emulsions, i.e., liquid core-shell structures, is still challenging. Here, we demonstrate a novel double-step emulsification method for the direct generation of multi-core double-emulsions and provide a predictive model for the number of cores. While the mechanism of the formation of the core droplets or empty shell droplets follows the well-established scenario of simple step emulsification, the formation of double-emulsion droplets is strongly affected by the presence of the cores. Passing of the cores through the narrowing neck of the shell postpones shell pinch-off. In particular, we demonstrate that our system can be used for the generation of arbitrary large, tightly packed droplet clusters consisting of a controllable number of droplets. Finally, we discuss the options of upscaling the system for high-throughput generation of tailored double emulsions.