Floquet engineering is a powerful technique using periodic potentials, typically laser light, to drive materials into regimes inaccessible in equilibrium. Here, we show that Kondo models can be driven to multi-channel degenerate points, even when the starting model is single-channel. These emergent channels are differentiated by symmetry, and their strength and number can be controlled by changing the light polarization, frequency and amplitude. Unpolarized light, constructed by polarization averaging, is particularly useful to induce three and four channel degeneracies. Multi-channel Kondo models host a wide variety of exotic phenomena, including non-Abelian anyons in impurity models and composite pair superconductivity in lattice models. We demonstrate our findings on both a simple square lattice toy model and a more realistic spin-orbit coupled model for $J=5/2$ Ce ions in a tetragonal environment, as relevant for the Ce 115 materials, and show that the transition temperature for composite pair superconductivity can be dynamically enhanced.

19 pages including Appendices, 10 figures