In principle this can work and already have the request to “restart” and already done run, especially for fluid mechanics simulations. There it is very common in a not-yet-converged stationary analysis to restart it (possibly with modified parameters) to do some more iterations until convergence.
This is would need a rather big development effort as it contradicts our current paradigm that a simulation run is immutable. This could be overcome by chaining simulation runs, using the previous one as initial condition for the new run. This is on our road map already, but nothing for short term release.
The solution with the user defined fields would be a rather quick solution. It’s already on the feature request list and starting to increase its priority