This short article presents an abstract, tunable model of genomic structural change within the cell life cycle and explores its use with simulated evolution. A well-known Boolean model of genetic regulatory networks is extended to include changes in node connectivity based upon the current cell state to begin to capture some of the effects of transposable elements. The evolvability of such networks is explored using a version of the NK model of fitness landscapes with both synchronous and asynchronous updating. Structural dynamism is found to be selected for in nonstationary environments with both update schemes and subsequently shown capable of providing a mechanism for evolutionary innovation when such reorganizations are inherited. This is also found to be the case in stationary environments with asynchronous updating.