Group identity is known to exert a powerful socio-psychological influence on behaviour but to date has been largely explored as a uni-dimensional phenomenon. We consider the role of multiple dimensions of identity, asking what might happen to ingroup and outgroup perceptions and the resulting implications for cooperation. Carefully selecting two politically charged identity dimensions documented to have similar strength and to be largely orthogonal (religious belief and views about government size), we find that priming individuals to consider both dimensions rather than one has a noticeable effect on behaviour. Moving from one to two dimensions can produce a significant increase in ingroup allocations at the expense of fairness to outgroup individuals, although the effect varies as we switch from primarily considering religion to government size. Evidence suggests that the heterogeneity of such effects is related to the degree of "harmony" between groups in the dimensions concerned.