Human hematopoiesis is surprisingly resilient to disruptions, providing suitable responses to severe bleeding, long-lasting immune activation, and even bone marrow transplants. Still, many blood disorders exist which push the system past its natural plasticity, resulting in abnormalities in the circulating blood. While proper treatment of such diseases can benefit from understanding the underlying cell dynamics, these are non-trivial to predict due to the hematopoietic system's hierarchical nature and complex feedback networks. To characterize the dynamics following different types of perturbations, we investigate a model representing hematopoiesis as a sequence of compartments covering all maturation stages-from stem to mature cells-where feedback regulates cell production to ongoing necessities. We find that a stable response to perturbations requires the simultaneous adaptation of cell differentiation and self-renewal rates, and show that under conditions of continuous disruption-as found in chronic hemolytic states-compartment cell numbers evolve to novel stable states.