Baystate Health, which runs Baystate Medical Center in Springfield and bills itself as the largest healthcare organization in Western Massachusetts, announced a leadership shake-up on Tuesday and said more changes are to come. The announcement came as the organization, which serves the Pioneer Valley and surrounding areas, tries to stanch the financial bleeding that has plagued many hospitals in recent years. Peter D. Banko, who became the new CEO of the system in June, said in a note to staff that three senior vice presidents will be leaving the organization effective Oct. 23. They are Kevin Conway, chief information and digital officer; Kristin Morales-Lemieux, chief human resources officer; and Doug Salvador, chief quality officer. Banko thanked them for their work and gave no explanation for why they are departing.