How to get maximum damping factor from this system?
The damping factor of a complex pair of poles (roots of the characteristic equation) is defined using the the pole position within the complex s-plane. If the angle between the negative-real axis and the pointer to the pole is "alpha" the damping factor d is defined as d=cos(alpha). 

It is obvious that cos(alpha) can be expressed by the real part of the pole and the pole frequency (magnitude of the pointer to the pole position). 

This definition concerns the complex pole pair only and is, thus, independent on a third pole on the negative-real axis or any zeros of the function. 

More than that, the "pole quality factor" Qp is defined as Qp=1/2d.

Hence, for poles in the left half of the s-plane (stable systems) the damping factor varies between "1" and "0" and the pole Qp between "1/2" and "infinite" (oscillation condition).