Dynamic Compensator in Control Loop
Gain scheduling is the term you're looking for.

As long as the transition is instantaneous, what's going to happen is that you'll get a glitch on the output that's filtered by C2.

As long as you make the transition at a point when the loop is stable, you'll be going from a stable system to a stable system, and you'll have no problem.  Even if you switched after you got into "run" mode, you'd still be switching to a stable system and you'd have no problem.