  We show that the essential properties of a Feshbach resonance in cold atomic
gases can be tuned by dressing the atomic states in different scattering
channels through inter-channel couplings. Such a scheme can be readily
implemented in the orbital Feshbach resonance of alkaline-earth-like atoms by
coupling hyperfine states in the clock-state manifolds. Using $^{173}$Yb atoms
as an example, we find that both the resonance position and the two-body
bound-state energy depend sensitively on the inter-channel coupling strength,
which offers control parameters in tuning the inter-atomic interactions. We
also demonstrate the dramatic impact of the dressed Feshbach resonance on
many-body processes such as the polaron to molecule transition and the BCS-BEC
crossover.
