We study the Flying Sidekick Traveling Salesman Problem with Multiple Drops (FSTSP-MD), a multi-modal last-mile delivery model where a single truck and a single drone cooperatively deliver customer packages. In the FSTSP-MD, the drone can be launched from the truck to deliver multiple packages before it returns to the truck for a new delivery operation. The objective is to find the synchronized truck and drone delivery routes that minimize the completion time of the delivery process. We develop a simple and effective heuristic to solve the FSTSP-MD based on an order-first, split-second scheme. This heuristic combines standard local search and diversification techniques with a novel shortest-path problem that finds FSTSP-MD solutions in polynomial time. We show that our heuristic consistently outperforms state-of-the-art heuristics developed for the FSTSP-MD and the FSTSP (i.e., the single-drop case) through extensive numerical experiments. Based on both stylized and real-world instances, we also show that the FSTSP-MD substantially reduces completion times compared to traditional truck-only delivery systems. We provide extensive managerial insights into the impacts of drone capabilities and customer distribution on delivery efficiency. Our discussion compares the benefits of drones with greater payload capacity and those with greater speed. We highlight which service area characteristics increase savings but also require enhanced drone capabilities.