Estimating the conditional average treatment effect (CATE) from observational data is relevant for many applications such as personalized medicine. Here, we focus on the widespread setting where the observational data come from multiple environments, such as different hospitals, physicians, or countries. Furthermore, we allow for violations of standard causal assumptions, namely, overlap and unconfoundedness. To this end, we move away from point identification and focus on partial identification. Specifically, our contributions are three-fold: (1) We derive bounds for the CATE where we leverage changes in the treatment assignment mechanism across environments. (2) We propose different meta-learners to estimate the bounds. Importantly, our meta-learners are model-agnostic and can be used in combination with any machine learning model. (3) We show theoretically that our meta-learners have desirable properties, such as consistency and doubly robustness. We further demonstrate the effectiveness of our meta-learners across various experiments using both simulated and real-world data. While there is rich literature on the \emph{derivation} of CATE bounds, a unique focus of our work is that we contribute learners for the \emph{estimation} of such bounds. Finally, we discuss the applicability of our meta-learners to partial identification in instrumental variable settings, such as randomized controlled trials with non-compliance.