Excess Gibbs energy models are often fitted to binary experimental data of phase equilibria. Even in the case of two binary parameters fitted to two binary infinite-dilution activity coefficients, multiple solutions for the parameters may occur. The present work shows that this is also true, if more data - like vapor-liquid equilibrium data sets - is used. Chemical systems and conditions are identified that lead to multiple solutions. It is shown that the multiple solutions may lead to significantly different results when the models are used in simulation of separation processes.