When faced with a large number of related tasks, like clearing unread emails or tackling a mountain of laundry, it’s often most efficient to handle them together as a single batch. The si ple observation is that grouping similar tasks together can ultimately streamline the entire process. In the context of Information Retrieval, batch processing has been applied to the problem of conjunctive querying by re-using partially computed results to avoid redundant list intersections or disk reads, reducing the total computational effort required to answer the given query batch. However, there has yet to be any work on exploiting batch query processing in the context of disjunctive querying semantics, which are often implemented by highly optimized top-$k$ dynamic pruning algorithms. In this work, we explore two simple yet efficient approaches to reduce the computational cost of top-$k$ querying in the batch processing regime. Our experimentation on two collections, and two unique query batches, demonstrates end-to-end cost reductions of up to 44% over standard query processing algorithms, and lays the foundation for future work towards more sophisticated top-$k$ batch querying techniques.