It is well known that a controllable nonlinear system will retain its controllabality when new actuator inputs are added to it. In this article, we ask the question if a system, linearisable by static or dynamic feedback, will retain this property when new actuator inputs are added to it. Alternatively, a system may be linearisable after removing one or more inputs from it. This question is important in the design of robotic systems from the perspective of trajectory planning and control, specially if they are under-actuated. The goals of this article are as follows: (i) using counter examples, we first show that feedback linearisability may not be preserved when new inputs are added to a robotic system, (ii) sufficient conditions are determined when a system will retain this property under the addition of new inputs. The theory is illustrated through some examples from the robotics field.