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We propose a new method of unification introducing a Spin-Foam model representing both the gravitational and the Yang-Mills degrees of freedom. To present a calculable example, we realize a unification between an SU(2) Yang-Mills interaction and 3D general relativity by considering a Spin(4)∼SO(4) 3D Plebanski action. The theory is then quantized a' la Spin-Foam by implementing the analogue of the simplicial constraints for the broken phase of the Spin(4) symmetry. Although our results are presented in 3D, we show how a similar procedure can be implemented in 4D. We also present two-point functions between the connections belonging to the two SU(2) cosets of the theory and define how to implement the scattering between particle states in this research program aiming to connect Loop Quantum Gravity to possible physical predictions.