Changing a class of properties in a custom component at design time

I am writing a simple component. I want to ensure that my MethodOptions methods change in the Object Inspector according to my chosen method.

Something like that:

So far I have encoded:

  TmyMethod = (cmFirst, cmSecond);

   TmyMethodOptions = class(TPersistent)    
    published
        property SomethingInBase: boolean;
   end;

   TmyMethodOptionsFirst = class(TmyMethodOptions)
    published
        property SomethingInFirst: boolean;
   end;

   TmyMethodOptionsSecond = class(TmyTMethodOptions)
    published
        property SomethingInSecond: boolean;
   end;

  TmyComponent = class(TComponent)
    private
      fMethod: TmyMethod;
      fMethodOptions: TmyMethodOptions;
      procedure ChangeMethod(const Value: TmyMethod);
    public
      constructor Create(AOwner: TComponent); override;
      destructor Destroy; override;
    published
      property Method: TmyMethod read fMethod write ChangeMethod default cmFirst;
      property MethodOptions: TmyMethodOptions read fMethodOptions 
        write fMethodOptions;  
  end;

implementation

procedure TmyComponent.ChangeMethod(const Value: TmyMethod);
begin
  fMethod := Value;

  fMethodOptions.Free;
  // case...
  if Value = cmFirst then
    fMethodOptions := TmyMethodOptionsFirst.Create
  else
    fMethodOptions := TmyMethodOptionsSecond.Create;

//  fMethodOptions.Update;
end;

constructor TmyComponent.Create(AOwner: TComponent);
begin
  inherited;
  fMethodOptions := TmyMethodOptions.Create;

  fMethod := cmFirst;
end;

destructor TmyComponent.Destroy;
begin
  fMethodOptions.Free;

  inherited;
end;

Of course, it has almost nothing (other than a hanging IDE), and I don't have any starting point for finding the right knowledge to achieve this.