Empirical research on \textit{construals}--social affinity groups that share similar patterns of meaning--has advanced significantly in recent years. This progress is largely driven by the development of \textit{Construal Clustering Methods} (CCMs), which group survey respondents into construal clusters based on similarities in their response patterns. We identify key limitations of existing CCMs, which affect their accuracy when applied to the typical structures of available data, and introduce Bipolar Class Analysis (BCA), a CCM designed to address these shortcomings. BCA measures similarity in response shifts between expressions of support and rejection across survey respondents, addressing conceptual and measurement challenges in existing methods. We formally define BCA and demonstrate its advantages through extensive simulation analyses, where it consistently outperforms existing CCMs in accurately identifying construals. Along the way, we develop a novel data-generation process that approximates more closely how individuals map latent opinions onto observable survey responses, as well as a new metric to evaluate the performance of CCMs. Additionally, we find that applying BCA to previously studied real-world datasets reveals substantively different construal patterns compared to those generated by existing CCMs in prior empirical analyses. Finally, we discuss limitations of BCA and outline directions for future research.