The related concepts of partisan belief systems, issue alignment, and partisan sorting are central to our understanding of politics. These phenomena have been studied using measures of alignment between pairs of topics, or how much individuals' attitudes toward a topic reveal about their attitudes toward another topic. We introduce a higher-order measure that extends the assessment of alignment beyond pairs of topics by quantifying the amount of information individuals' opinions on one topic reveal about a set of topics simultaneously. Applying this approach to legislative voting behavior shows that parliamentary systems typically exhibit similar multiway alignment characteristics, but can change in response to shifting intergroup dynamics. In American National Election Studies surveys, our approach reveals a growing significance of party identification together with a consistent rise in multiway alignment over time.