Many practical systems are non-deterministic, in the sense that available information about the initial states and control values does not uniquely determine the future states. For some such systems, it is important to take quantum effects into account. For that, we need to develop non-deterministic versions of quantum physics. In this paper, we show that for non-deterministic versions of quantum physics, we cannot require superposition principle -- one of the main fundamental principles of modern quantum mechanics. Specifically, while we can consider superpositions of states corresponding to the same version of the future dynamics, it is not consistently possible to consider superpositions of states corresponding to different versions of the future.