We study the Giant Magnetoresistance (GMR) ratio in magnetic multiayers with a single superconducting contact in the presence of spin-mixing processes. It has been recently shown that the GMR ratio of magnetic multilayers is strongly suppressed by the presence of a superconducting contact when spin-flipping is not allowed. In this Letter we demonstrate that the GMR ratio can be dramatically enhanced by spin-orbit interaction and/or non-collinear magnetic moments. The system is described using a

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... tight-binding model with either s-p-d or s-d atomic orbitals per site.