In the viscoelastic Taylor-Couette flow, it is known that at certain parameter values, the onset condition can involve more than one mode becoming unstable. We focus on the upper convected Maxwell liquid, and on the situation where two Hopf modes, or a Hopf mode and a steady mode, are simultaneously at criticality. The interaction of such modes is investigated at critical situations. Weakly non-linear amplitude equations are derived for the interaction of these modes, based on a center manifold reduction scheme. The two modes generate a two-parameter bifurcation. The coefficients involved in the equations are determined numerically, based on the physical parameters of the system at criticality. For the cases investigated, it is found that all the bifurcated branches of solutions are unstable. Moreover, direct numerical simulation of the amplitude equations does not lead to bounded solutions.