The 2014 "Standards for Educational and Psychological Testing" describe universal design as an approach that offers promise for improving the fairness of educational assessments. As the field reconsiders questions of fairness in assessments, we propose a new framework that addresses the entire assessment lifecycle: universal design of assessment systems. This framework is rooted in the original Universal Design principles but extends beyond test design and administration to the entire assessment lifecycle, from construct definition to score interpretation and use. Another core tenet within this framework is the integration of psychological theory on universal human needs for autonomy, competence, and relatedness with flexibility based on our contemporary understandings of neurodiversity, culture, and multilingualism. Finally, the framework integrates the original "Universal Design" principle of "tolerance for error," which promotes assessment designs that anticipate unintended actions and mitigate potential harms. After describing how the principles and guidelines might apply in contexts ranging from classroom assessments to statewide assessments and licensure exams, we conclude with practical implications and next steps. We hope future versions of the "Standards for Educational and Psychological Testing" incorporate this broader, systems-wide approach to universal design.