Affective polarization has been central to political and social studies, with growing focus on social media, where partisan divisions are often exacerbated. Real-world studies tend to have limited scope, while simulated studies suffer from insufficient high-quality training data, as manually labeling posts is labor-intensive and prone to subjective biases. The lack of adequate tools to formalize different definitions of affective polarization across studies complicates result comparison and hinders interoperable frameworks. We present a multi-agent model providing a comprehensive approach to studying affective polarization in social media. To operationalize our framework, we develop a platform leveraging large language models (LLMs) to construct virtual communities where agents engage in discussions. We showcase the potential of our platform by (1) analyzing questions related to affective polarization, as explored in social science literature, providing a fresh perspective on this phenomenon, and (2) introducing scenarios that allow observation and measurement of polarization at different levels of granularity and abstraction. Experiments show that our platform is a flexible tool for computational studies of complex social dynamics such as affective polarization. It leverages advanced agent models to simulate rich, context-sensitive interactions and systematically explore research questions traditionally addressed through human-subject studies.