Chronic myeloid leukemia (CML) is a blood cancer in which there is dysregulation of maturing myeloid cells (granulocytes) driven by a chromosomal mutation which creates the fusion gene, BCR-ABL1. Although there has been much progress in the treatment of CML using tyrosine kinase inhibitors (TKI), there are still unmet clinical needs. For example, there is still a small cohort of patients who, for reasons that are still unknown, do not respond to TKI treatment. Further, a significant proportion of patients who appear to have a complete molecular remission while on TKIs experience a relapse of CML when TKI treatment is discontinued. Mathematical modeling of CML hematopoiesis can provide insight on these processes. Current mathematical models of CML are highly simplified (e.g., linear) and have been used to estimate treatment-related model parameters, but fail to describe the mechanisms that underlie primary resistance and treatment-free remission. Here, we explore how more physiologically accurate, data-driven mathematical models of CML hematopoiesis that incorporate feedback control and lineage branching can provide such insight. Although it is recognized that feedback plays a role in CML hematopoiesis, the interactions are poorly understood. In many cases, we don’t know which cell types are providing and receiving the feedback, what signals are used, and what aspects of proliferative cell behavior they influence (i.e. cell cycle speed, renewal probability, or progeny fate choice). Here, we propose to use mathematical modeling combined with data from single cell transcriptomics to help sort this out. We develop an automated method for model selection that integrates data gleaned from experiments and single cell RNA sequencing to select plausible classes of feedback models. We first apply this approach to normal hematopoiesis and identify models that have desired system properties, e.g., stable equilibria, and make predictions about system behavior upon perturbation. New experiments are presented that validate model predictions. We use a Bayesian utility theory approach to determine the optimal experimental design that allows for identification of model parameters with maximum precision. When extended to incorporate CML hematopoiesis, our initial assessment shows that feedback/branching models are more robust, have a better fit to alternative patterns of patient response than simple linear models, and suggest new treatment strategies.