Existing work on Counterfactual Explanations (CE) and Algorithmic Recourse (AR) has largely focused on single individuals in a static environment: given some estimated model, the goal is to find valid counterfactuals for an individual instance that fulfill various desiderata. The ability of such counterfactuals to handle dynamics like data and model drift remains a largely unexplored research challenge. There has also been surprisingly little work on the related question of how the actual implementation of recourse by one individual may affect other individuals. Through this work, we aim to close that gap. We first show that many of the existing methodologies can be collectively described by a generalized framework. We then argue that the existing framework does not account for a hidden external cost of recourse, that only reveals itself when studying the endogenous dynamics of recourse at the group level. Through simulation experiments involving various state-of-the-art counterfactual generators and several benchmark datasets, we generate large numbers of counterfactuals and study the resulting domain and model shifts. We find that the induced shifts are substantial enough to likely impede the applicability of Algorithmic Recourse in some situations. Fortunately, we find various strategies to mitigate these concerns. Our simulation framework for studying recourse dynamics is fast and open-sourced.@en