Prepositioning is a critical disaster preparedness mechanism for humanitarian organizations (HOs) but requires significant investment. Improving the efficiency of prepositioned stocks is a primary concern within the humanitarian community. This study, conducted in collaboration with the Emergency Supply Prepositioning Strategy (ESUPS) Working Group, examines the impact of implementing postponement and stock‐sharing strategies in a regional humanitarian warehouse. We focus on a setting where multiple HOs preposition supplies within the same warehouse to serve disaster‐affected countries. Traditionally, these prepositioned supplies are branded with the respective HOs' logos, hindering the sharing of surplus stock during disaster response. Our system defers the branding process for a portion of the stockpile until after a disaster, facilitating the sharing of unbranded stock among HOs. To evaluate the benefits of postponement in this humanitarian context, we develop a two‐phase inventory allocation framework for distributing branded and unbranded stocks to disaster‐affected countries and for sharing unbranded stocks among HOs. We then incorporate our inventory allocation models into a Monte Carlo simulation algorithm that accounts for uncertainties regarding the occurrence and impact of disasters. Using a case study based on data from ESUPS members in the Caribbean region, we demonstrate that the proposed strategy can significantly enhance the efficiency and effectiveness of prepositioning. Remarkably, we observe a U‐shaped relationship in response time as the postponement rate increases, while the fill rate and inventory utilization consistently improve. Our numerical study provides valuable insights for decision making in humanitarian logistics.