Medicine is increasingly focusing on the prevention of diseases. The digital twin (DT) is considered to be an important technological development for realizing this transition. Broadly speaking, a DT is an in silico representation of an individual that dynamically reflects molecular and physiological status, which makes it possible to monitor precisely health status over time. Currently, DTs are more of an abstract ideal than a concrete technological reality, which makes it possible to actively imagine the different ways in which DTs might materialize. This article develops an approach to imagining the different ways in which DTs can be integrated into the lives of people. It focuses on how potential users want to be cared for by means of DTs and how care practices might be changed through the introduction of DTs. The article shows that a shift towards preventive medicine is taking place and situates DT in this context. Then, drawing on the insights of Gilbert Simondon, it suggests that the notion of technical milieu can be a helpful tool for designers to imagine the practices of valuing to which DTs give rise. Subsequently, it explains how our philosophical approach helps inform what kinds of DTs can be imagined. Then, based on interviews with people likely to relate to DTs in the (near) future, it develops six conceptions of DTs and fleshes out some of the implications of our approach for the design of DTs.