There is a growing body of work considering the use of representations based upon genetic regulatory networks. This paper uses a recently presented abstract, tunable Boolean regulatory network model to explore aspects of mobile DNA, such as transposons, within these dynamical systems. The significant role of mobile DNA in the evolution of natural systems is becoming increasingly clear. Whilst operators loosely based upon transposons have previously been used within evolutionary computation, their use within regulatory network representations enables the potential exploitation of numerous new mechanisms. This paper shows how dynamically controlling network node connectivity and function via transposon-inspired mechanisms can be selected for under non-stationary and coevolutionary scenarios, including when such changes are heritable.