Plasticity enables cells to change their gene expression state in the absence of a genetic change.At the single-cell level, gene expression states can persist for different lengths of time, which is a quantitative measurement referred to as gene expression memory. Because plasticity is not encoded by genetic changes, these states can be reversible, and therefore, are amenable to modulation by disrupting gene expression memory. However, we currently do not have robust methods to find the regulators of memory or to track state switching in plastic cell populations. Here, we developed a lineage tracing-based technique to quantify gene expression memory and to identify cells undergoing state switching. Applied to human melanoma cells, we quantified long-lived fluctuations in gene expression states that underlie resistance to targeted therapy. Further, we identified the PI3K and TGF-β pathways as modulators of these state switching dynamics. Leveraging the PI3K and TGF-β pathways as dials on switching between plastic states, we propose a "pretreatment" model in which we first use a PI3K inhibitor to modulate the gene expression states of the cell population and then apply targeted therapy. This plasticity-informed dosing scheme ultimately leads to less drug resistance than targeted therapy alone. Taken together, we describe a technique to find modulators of gene expression memory and then apply this knowledge to alter plastic cell states and their connected cell fates.