Many language proficiency tests include group oral assessments involving peer interaction. In such an assessment, examinees discuss a common topic with others. Human raters score each examinee's spoken performance on specially designed criteria. However, measurement models for analyzing group assessment data usually assume local person independence and thus fail to consider the impact of peer interaction on the assessment outcomes. This research advances an extended many-facet Rasch model for group assessments (MFRM-GA), accounting for local person dependence. In a series of simulations, we examined the MFRM-GA's parameter recovery and the consequences of ignoring peer interactions under the traditional modeling approach. We also used a real dataset from the English-speaking test of the Language Proficiency Assessment for Teachers (LPAT) routinely administered in Hong Kong to illustrate the efficiency of the new model. The discussion focuses on the model's usefulness for measuring oral language proficiency, practical implications, and future research perspectives.