Spring-mass systems are known to experience vortex-induced vibrations (VIV) when exposed to viscous flows. These vibrations can be efficiently used for energy generation in ocean currents and rivers because significant power density can be extracted even from moderate flow velocities. The VIV generators typically include a large system of vertical or horizontal cylinders aligned perpendicular to the flow. The cylinders are connected elastically to a fixed frame and can oscillate independently. A recent comparative study shows that the VIV generators compete well with other renewable energy sources and clean technologies. This manuscript presents a new technique aiming to increase further the efficiency of the VIV energy generators by introducing some coupling between the motions of their cylindrical members. The VIV of circular cylinders is evaluated with CFD simulations. The motions of independently oscillating cylinders are compared to the motions of elastically interconnected cylinders. The numerical analysis shows that the motion amplitudes can be amplified significantly with suitable elastic interconnections between the cylinders. The proposed approach requires designing various VIV frequencies for the different members of the system, which does not allow them to synchronize their phases, and introduces instability in the motion patterns. The elastic interconnections can increase the efficiency of the green energy generation between 10% and 20% compared to previously proposed similar systems.