A new cooperative interference harnessing technique is proposed for non-orthogonal multiple access (NOMA) aided downlink multicell networks. The technique, coined as cooperative successive interference cancellation (Coop-SIC), leverages on the optimality conditions for SIC in the multiple access channel (MAC) seen at the receiver side without superposition coding at the transmitter. We derive SIC gain conditions that determine when is beneficial to reduce one user's rate in order to enable SIC in another user potentially increasing its rate and maximize the sum-rate. The sum-rate maximization problem in multicell downlink systems is formulated and an algorithm to find the optimal solution is provided. Our simulation results show that our Coop-SIC technique is employed up to 80% of the iterations, providing up to 40% gains in the network's spectral efficiency.