Understanding signaling patterns of transformation and controlling cell phenotypes is a challenge of current biology. Here we applied a cell State Transition Assessment and Regulation (cSTAR) approach to a perturbation dataset of single cell phosphoproteomic patterns of multiple breast cancer (BC) and normal breast tissue-derived cell lines. Following a separation of luminal, basal, and normal cell states, we identified signaling nodes within core control networks, delineated causal connections, and determined the primary drivers underlying oncogenic transformation and transitions across distinct BC subtypes. Whereas cell lines within the same BC subtype have different mutational and expression profiles, the architecture of the core network was similar for all luminal BC cells, and mTOR was a main oncogenic driver. In contrast, core networks of basal BC were heterogeneous and segregated into roughly four major subclasses with distinct oncogenic and BC subtype drivers. Likewise, normal breast tissue cells were separated into two different subclasses. Based on the data and quantified network topologies, we derived mechanistic cSTAR models that serve as digital cell twins and allow the deliberate control of cell movements within a Waddington landscape across different cell states. These cSTAR models suggested strategies of normalizing phosphorylation networks of BC cell lines using small molecule inhibitors.