Non-genetic transcriptional variability is a potential mechanism for therapy resistance in melanoma. Specifically, rare subpopulations of cells occupy a transient pre-resistant state characterized by coordinated high expression of several genes and survive therapy. How might these rare states arise and disappear within the population? It is unclear whether the canonical models of probabilistic transcriptional pulsing can explain this behavior, or if it requires special, hitherto unidentified mechanisms. We show that a minimal model of transcriptional bursting and gene interactions can give rise to rare coordinated high expression states, These states occur more frequently in networks with low connectivity and depend on three parameters. While entry into these states is initiated by a long transcriptional burst that also triggers entry of other genes, the exit occurs through independent inactivation of individual genes. Together, we demonstrate that established principles of gene regulation are sufficient to describe this behavior and argue for its more general existence. A record of this paper's transparent peer review process is included in the Supplemental Information.