In this article, multiple steady states are studied in sequences of interlinked columns commonly used to separate azeotropes in ternary homogeneous distillation. More specifically, two major separation schemes were concerned : the intermediate entrainer scheme and the "boundary separation" scheme. On the basis of the results on multiplicities in single columns for the case of infinite reflux and infinite column length (infinite number of trays) similar criteria for separation sequences were developed. It is shown how to construct bifurcation diagrams on physical grounds with one product flow rate as the bifurcation parameter and how the product paths of a sequence can be located. Moreover, a necessary and sufficient condition for the existence of multiple steady states in column sequences is derived on the basis of the geometry of the product paths. The overall feed compositions that lead to multiple steady states in the composition space are also located. For the intermediate entrainer scheme multiplicities occur for all feed compositions. For the boundary separation scheme multiplicities may disappear when a single column is integrated into a sequence. By use of examples df the two separation schemes, it is shown that the prediction of the existence of multiple steady states in the infinity/infinity case has relevant implications for columns with finite length (finite number of trays) operated at finite reflux.