We have studied the endemic steady state stability properties for a multistrain epidemic model on two migration-coupled patches. Interactions between strains in the model were governed by temporary partial cross immunity and antibody-dependent enhancement. In the absence of coupling, the system displayed Hopf bifurcations in two epidemic parameters. Coupling between patches with non-identical parameters, which gave them non-identical characteristic frequencies of oscillation, was shown to shift the Hopf bifurcations, stabilizing the steady state. This behavior was observed for the Hopf bifurcation obtained by sweeping the cross immunity in the absence of ADE and the bifurcation obtained by sweeping the ADE in the absence of cross immunity. It occurred for asymmetry in either of our two social parameters, the birth rate and the contact rate.