In some patients with myeloproliferative neoplasms (MPN), two genetic mutations are often found, JAK2 V617F and one in the TET2 gene. Whether or not one mutation is present will influence how the other subsequent mutation affects the regulation of gene expression. When both mutations are present, the order of their occurrence has been shown to influence disease progression and prognosis. We propose a nonlinear ordinary differential equation (ODE), Moran process, and Markov chain models to explain the non-additive and non-commutative mutation effects on recent clinical observations of gene expression patterns, proportions of cells with different mutations, and ages at diagnosis of MPN. These observations consistently shape our modeling framework. Our key proposal is that bistability in gene expression provides a natural explanation for many observed order-of-mutation effects. We also propose potential experimental measurements that can be used to confirm or refute predictions of our models.