Set the parameters for the StepFunction in a G4VPhysicsConstructor

I am using a custom G4VModularPhysicsList to register a custom (em) ‘Physics’ class (inheriting from G4VPhysicsConstructor) with the command RegisterPhysics(new Physics());
I would like the parameters for the StepFunction of this Physics not to be hard-coded, but I didn’t find a good way to pass it to the class, as the ConstructProcess() function does not accept arguments and even the class constructor is not allowed to have a different signature from the base class constructor (otherwise the RegisterPhysics() call causes a compilation error).

How is one supposed to pass parameters to G4VPhysicsConstructor classes without resorting to global variables? Is there a way to call SetStepFunction() after the physics lists have already been initialized?

P.S: I do not use a UI.