The Upper Basin of the Colorado River in the southwestern United States supports municipal, industrial, agricultural, and recreational activities worth an estimated $300 billion/year within the state of Colorado alone. The allocation of water to these activities is fundamentally shaped by water rights that in turn distribute risks among a diverse suite of sectors and stakeholders. In this study, we assess the vulnerabilities faced by the hierarchy of hundreds of water users in the portion of the Upper Basin within the state of Colorado, as a result of changes in hydrologic extremes, demand growth, and institutional and physical infrastructure in the basin. We also determine how robust the different users are to these potential changes, examining how their sensitivity to these factors depends on the magnitude and frequency of shortage they are unwilling to exceed. This advances previous robustness evaluation methods by formalizing an a posteriori exploration of alternative definitions of robustness tailored to each user's unique context. Our analysis reveals that robustness varies significantly not only across users but also across different definitions of acceptable performance for each user. We further show the importance of using scenario discovery to evaluate how the factors that drive consequential scenarios differ depending on the definition of robustness. Our results highlight the need for robustness and vulnerability frameworks to avoid broad categorical aggregations of stakeholder groups, to carefully capture complex institutional dependencies (e.g., water rights), and to facilitate a more transparent illustration of the implications of alternative definitions of robustness for specific stakeholders.