Users often rely on Large Language Models (LLMs) for processing multiple documents or performing analysis over a number of instances. For example, analysing the overall sentiment of a number of movie reviews requires an LLM to process the sentiment of each review individually in order to provide a final aggregated answer. While LLM performance on such individual tasks is generally high, there has been little research on how LLMs perform when dealing with multi-instance inputs. In this paper, we perform acomprehensive evaluation of the multi-instance processing (MIP) ability of LLMs for tasks in which they excel individually. The results show that all LLMs follow a pattern of slight performance degradation for small numbers of instances (≈20–100), followed by a performance collapse on larger instance counts. Crucially, our analysis shows that while context length is associated with this degradation, the number of instances has a stronger effect on the final results. This finding suggests that when optimising LLM performance for MIP, attention should be paid to both context length and, in particular, instance count.