A series of homotopic continuation studies are presented that explore steady state multiplicities in a reactive distillation column producing ethylene glycol from ethylene oxide and water. The glycol column has two sets of multiplicities : a three-branch multiplicity that occurs at large values of the holdup volume and a complex switchbacking multiplicity that occurs at small values of the holdup volume. The optimal column has three steady states, and at small holdup volumes, the column can have as many as nine steady states. The computational studies show that the multiplicities are not affected by feed or holdup volume distribution and are not caused by multiple reactions, the temperature dependency of the reaction rate, or the exothermic heat of reaction. The three-branch multiplicity arises from coupling between the bilinear reaction rate and the large volatility differences between the reactants. Analytical results show that the lower turning point of this multiplicity occurs when the oxide feed has been consumed and water begins to accumulate in the vapor boilup streams. The upper turning point of the multiplicity takes place via a series of complex switchbacks that create a second set of multiplicities. This switchbacking multiplicity is more complex, and is influenced by the reactant volatility difference and the kinetic reaction rate constants.