Here, we focus on a common class of enzymes that have multiple substrate binding sites (multisite enzymes) and analyze their capacity to generate bistable dynamics in the reaction networks that they are embedded in. These networks include both substrate-product-substrate cycles and substrate-to-product conversion with subsequent product consumption. Using mathematical techniques, we show that the inherent binding and catalysis reactions arising from multiple substrate-enzyme complexes create a potential for bistable dynamics in such reaction networks. We construct a generic model of an enzyme with n-substrate binding sites and derive an analytical solution for the steady-state concentration of all enzyme-substrate complexes. By studying these expressions, we obtain a mechanistic understanding of bistability, derive parameter combinations that guarantee bistability, and show how changing specific enzyme kinetic parameters and enzyme levels can lead to bistability in reaction networks involving multisite enzymes. Thus, the presented findings provide a biochemical and mathematical basis for predicting and engineering bistability in multisite enzymes.