We study the plasticity of a delayed stochastic model of a genetic toggle switch as a multipotent differentiation pathway switch, at the single cell and cell population levels, by observing distributions of differentiation pathways choices of genetically homogeneous cell populations. Assuming a model of stochastic pathway determination of cell differentiation that is regulated by the proteins of the switch, we vary the proteins' expression level and degradation rates, which cells are known to be able to regulate, to vary mean level, noise, and bias of the proteins' expression levels. It is shown that small changes in each of these dynamical features significantly and distinctively affects the dynamics of the switch at the single cell level and thus, the cell differentiation patterns. The regulation of these features allows cells to regulate their pluripotency and cell populations' distribution of lineage choice, suggesting that the stochastic switch has high plasticity regarding differentiation pathway choice regulation, thus providing adaptability to environmental stresses and changes.