Video games are a special type of software that differ from other types of software systems in that they aim to deliver immersive experiences to users. As a result, issue reports (e.g., bug reports) in video game projects may require iterative fixes that span multiple pull requests (PRs). A PR is a mechanism in distributed version control systems (e.g., GitHub) through which developers propose code changes for review, discussion, and eventual integration into the main codebase. We refer to an issue report that is linked to multiple PRs as a multi-PR issue. Despite their potential impact on development efforts and coordination, such multi-PR issues remain largely unexplored. In this paper, we present a large-scale empirical study of multiPR issues in open-source game development. We analyze their prevalence, derive a taxonomy explaining why multiple PRs are associated with a single issue, and compare their resolution timelines and development effort against single-PR issues, i.e., issues resolved through exactly one PR. Our results show that approximately 5% of issues are resolved through multiple PRs. Most of these cases arise from iterative refinement. Quantitatively, multi-PR issues take substantially longer to resolve, with a median resolution time four times higher than that of single-PR issues. They are also associated with moderately higher commit-level activity. Our findings have practical implications for both practitioners and researchers. For practitioners, multi-PR issues require more careful planning, as they involve higher commit-level effort and are more likely to experience prolonged resolution times, potentially threatening release schedules. Moreover, when multiple contributors independently submit PRs for the same issue, teams risk duplicated implementation effort and increased review overhead, underscoring the importance of early coordination mechanisms (e.g., ownership assignment or consolidation of parallel fixes). For researchers, our results highlight the need for empirical models and tools that explicitly account for iterative resolution patterns rather than assuming single-PR fixes. We further encourage researchers to extend our taxonomy to other domains, such as web and mobile applications.