A growing body of experimental evidence indicates a strong link between intratumoral heterogeneity and therapeutic resistance in cancer. In particular, tumor cells may survive therapy by switching their phenotypic identities to more resistant, drug-tolerant states. Computational models of phenotypic plasticity in response to cytotoxic therapy are needed: (1) to strengthen understanding of the interplay between phenotypic heterogeneity and therapeutic resistance, and (2) to identify potential strategies in silico that weaken resistance prior to in vitro testing. This work presents a linear time-invariant model of phenotypic state dynamics to deduce subpopulation-level behavior likely to affect temporal phenotypic composition and thus drug resistance. The model was identified under different therapeutic conditions with authentic biological data from a breast cancer cell line. Subsequent analysis suggested drug-induced effects on phenotypic state switching that could not be deduced directly from empirical observations. A bootstrap algorithm was implemented to identify statistically significant results: reduction in cell division under each therapeutic condition versus control. Further, Monte Carlo simulation was used to evaluate quality of model fit for two-way switching and net switching on synthetically generated data to determine the limitations of the latter assumption for subsequent modeling. Most importantly, the simple model structure initiated a control-theoretic approach for identifying promising combination treatments in silico to guide future laboratory testing.