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We describe the magnetization reversal processes in multilayer elongated Ni80Fe20(10 nm)/Au(t = 0 to 20 nm)/ Co(20 nm)/Si(001) nanorings. For a field applied in-plane along the long axis, the hysteresis loops display a two-step switching for both t = 0 nm and 2 nm, and a three-step switching for t = 10 nm and 20 nm. Onion-to-vortex and vortex-to-reverse onion state transitions occur for a thin Au spacer due to strong exchange coupling between the layers. For a thick Au spacer layer, the Ni80Fe20 layer switches first, then a two-step reversal of the Co, correlated with domain motion in the Ni80Fe20, occurs without the formation of vortex states as a result of magnetostatic interactions. There is a good agreement between the experimental results and micromagnetic simulations.