Does the cosmic microwave background recede at the speed of light? Is it possible it recedes even faster because of the stretching of space?
Well obviously the CMBR arrives (towards us, not receding) at us at the speed of light as it is a form of electromagnetic radiation and local velocities are not affected by expansion.
What I guess you may mean though is the surface of last scattering, which is the surface from which the CMBR that we receive at a given instant was emitted in the early Universe. This surface of course is no longer emitting CMBR in the present cosmological time and it is not a fixed (comoving) surface either as which surface we receive the CMBR from changes with time, however we can give a recession velocity to the comoving set of points which make up the surface of last scattering at any given instant.
In the standard model of cosmology, the Lambda-CDM model, the instantaneous surface of last scattering is receding from us at approximately 3.2c (i.e. a recession velocity 3.2 times the speed of light).