Plasticity is the potential for cells or cell populations to change their phenotypes and behaviors in response to internal or external cues. Plasticity is fundamental to many complex biological processes, yet to date there remains a lack of mathematical models that can elucidate and predict molecular behaviors in a plasticity program. Here, we report a new mathematical framework that models cell plasticity as a multi-step completion process, where the system moves from the initial state along a path guided by multiple intermediate attractors until the final state (i.e. a new homeostasis) is reached. Using omics time-series data as model input, we show that our method fits data well; identifies attractor states by their timing and molecular markers which are well-aligned with domain knowledge; and can make quantitative and time-resolved predictions such as the molecular outcomes of blocking a plasticity program from reaching completion, to an R2 of 0.53-0.63. We demonstrate that application of our model to primary patient-derived data can provide quantitative insights and predictions that may be useful in guiding further research and potential biomedical interventions.