Large language models (LLMs) exhibit strong general capabilities, but their deployment in high-stakes domains is hindered by their opacity and unpredictability. Recent work has taken meaningful steps towards addressing these issues by augmenting LLMs with post-hoc reasoning based on computational argumentation, providing faithful explanations and enabling users to contest incorrect decisions. However, this paradigm is limited to pre-defined binary choices and only supports local contestation for specific instances, leaving the underlying decision logic unchanged and prone to repeated mistakes. In this paper, we introduce ArgEval, a framework that shifts from instance-specific reasoning to structured evaluation of general decision options. Rather than mining arguments solely for individual cases, ArgEval systematically maps task-specific decision spaces, builds corresponding option ontologies, and constructs general argumentation frameworks (AFs) for each option. These frameworks can then be instantiated to provide explainable recommendations for specific cases while still supporting global contestability through modification of the shared AFs. We investigate the effectiveness of ArgEval on treatment recommendation for glioblastoma, an aggressive brain tumour, and show that it can produce explainable guidance aligned with clinical practice.