In this paper, the author reports a study into usefulness of polysemy in the 6-multiplexer problem. The study is based on integer linear programming models for the problem of obtaining optimal classifiers for that multiplexer problem. Two classifier designs are considered each of which determines outputs according to inputs and classifiers. One design is typical. In this design, one classifier has one action, and one classifier supports only one output. In the other design with polysemy, one classifier has votes for all actions, and one classifier may support multiple outputs. In both designs, majority voting by matching classifiers determines the output for the corresponding input. Integer linear programming models are developed for some problem settings which differ in the classifier design, the number of classifiers, and the usage of the default rule which does not care the input. Solving those models display that if the number of classifiers is 4 and the default rule is not permitted, the design with polysemy yields more effective classifier sets than the other design.