Numerical simulations investigating the interaction of co-existent 2/1 and 3/1 neoclassical tearing modes are presented. The results obtained from an initial value 3D toroidal code that solves a set of generalized reduced MHD equations exhibit a host of complex phenomena arising from the coupling of the two modes. These include a modification of the island saturation widths of the two modes, a significant modification in the perpendicular flow patterns in the vicinity of the islands, and the excitation of geodesic acoustic mode like oscillations that lead to concomitant oscillations in the kinetic and magnetic energies of the islands. These oscillations only occur in the presence of the neoclassical stress tensor contribution and are absent for two coupled classical tearing modes.