Well. "Cool" and efficiency don't very often go together.
I'm sure that multiple fans in tandem must have been tried and rejected long ago. I think this must be something to do with the speed of air across the blades and the necessity of keeping the tip speed reasonable to avoid turbulence.
Turbines, however, have several layers of blades but a turbofan engine only has one set of blades used for actual propulsion afaik.