We study an extension of job market signalling by introducing another dimension of private information. When two dimensions of attribute are intertwined in parameterizing preferences, the single crossing property no longer holds globally. In seeking the equilibrium prediction, the intuitive criterion and then the more stringent perfect sequentiality refinement are applied. The result depends on the extent to which the second characteristic affects the ability of education to signal. If the effect is mild, the equilibrium acquired is comparable to the separating outcome of the unidimensional benchmark. Otherwise, pooling must occur. This demonstrates that the problem of information transmission is more acute in a multidimensional environment.