General hospitals across the world are becoming larger (i.e., admitting more patients each year) and more complex (i.e., offering a wider range of services to patients with more diverse care needs). Prior work suggests that an increase in patient volume in a hospital service is associated with reduced costs per patient in that service. However, it is unclear how volume changes in one service affect the costs of the other services in the same hospital. This paper investigates such volume-cost spillover effects between elective and emergency admissions and across specialties, using condition-level panel data comprising all acute hospital trusts in England over a period of 10 years. We provide evidence that increased elective volume at a hospital is associated with an increase in the cost of emergency care (a negative spillover). Furthermore, for emergency admissions, we find evidence that increased emergency activity in one specialty is associated with lower costs of emergency care in other specialties (a positive spillover). By contrast, we find no evidence of spillover effects across specialties for elective admissions. We discuss the implications of these findings for individual hospital growth strategies and for the regional organization of hospital systems.