The determination of individual cell trajectories through a high-dimensional cell-state space is an outstanding challenge for understanding biological changes ranging from cellular differentiation to epigenetic responses of diseased cells upon drugging. We integrate experiments and theory to determine the trajectories that single BRAF^V600E mutant melanoma cancer cells take between drug-naive and drug-tolerant states. Although single-cell omics tools can yield snapshots of the cell-state landscape, the determination of individual cell trajectories through that space can be confounded by stochastic cell-state switching. We assayed for a panel of signaling, phenotypic, and metabolic regulators at points across 5 days of drug treatment to uncover a cell-state landscape with two paths connecting drug-naive and drug-tolerant states. The trajectory a given cell takes depends upon the drug-naive level of a lineage-restricted transcription factor. Each trajectory exhibits unique druggable susceptibilities, thus updating the paradigm of adaptive resistance development in an isogenic cell population.