It is well known that given a controllable system, addition of new actuators cannot make the system to loose the controllability property. For linear systems, since controllability is equivalent to differential flatness, the latter property cannot be lost by addition of new inputs. However, this is not true for nonlinear systems. In this paper, we investigate under which conditions systems that are perturbed by addition of new inputs retain the property of being linearizable by static feedback linearization. Some sufficient conditions and a necessary one are given. The theory is illustrated with some examples