Identifying effective therapeutic treatment strategies is a major challenge to improving outcomes for patients with breast cancer. To gain a comprehensive understanding of how clinically relevant anti-cancer agents modulate cell cycle progression, here we use genetically engineered breast cancer cell lines to track drug-induced changes in cell number and cell cycle phase to reveal drug-specific cell cycle effects that vary across time. We use a linear chain trick (LCT) computational model, which faithfully captures drug-induced dynamic responses, correctly infers drug effects, and reproduces influences on specific cell cycle phases. We use the LCT model to predict the effects of unseen drug combinations and confirm these in independent validation experiments. Our integrated experimental and modeling approach opens avenues to assess drug responses, predict effective drug combinations, and identify optimal drug sequencing strategies.