Many water-soluble polymers are chemically modified versions of insoluble base materials such as cellulose. A Flory-Huggins model is solved to determine the effects of heterogeneity in modification on the solubility of such polymers. It is found that heterogeneity leads to decreased solubility, with the effect increasing with increasing blockiness. In the limit of extreme blockiness, the nature of the phase coexistence crosses over to a polymer-polymer demixing transition. Some consequences are discussed for the synthesis of partially modified polymers and the experimental characterization of such systems.