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Recent studies have shown that capillary waves generated by the bursting of an oil drop at the water–air interface produces a daughter droplet inside the bath, while a part of it floats above it. Successive bursting events produce next generations of daughter droplets, gradually diminishing in size until the entire volume of oil rests atop the water–air interface. In this work, we demonstrate two different ways to modulate this process by modifying the constitution of the drop. First, we introduce hydrophilic clay particles inside the parent oil drop and show that it arrests the cascade of daughter droplet generation preventing it from floating over the water–air interface. Second, we show that bursting behavior can be modified by a compound water–oil–air interface made of a film of oil with finite thickness and design a regime map, which displays each of these outcomes. We underpin both of these demonstrations by theoretical arguments providing criteria to predict outcomes resulting therein. Finally, all our scenarios have a direct relation to control of oil–water separation and stability of emulsified solutions in a wide variety of applications, which include drug delivery, enhanced oil recovery, oil spills, and food processing, where a dispersed oil phase tries to separate from a continuous phase.