  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.
