unit main
....
var
  NextFormShowed: boolean = false;
  NextForm: TForm = nil;
....
procedure TForm1.ApplicationEvents1Idle(Sender: TObject;
  var Done: Boolean);
begin
  if not NextFormShowed and Assigned(NextForm) then begin
    NextFormShowed:=true;
    NextForm.ShowModal;
  end;
end;
 ------------------------------------
 
unit unit2
...
procedure TForm2.Button1Click(Sender: TObject);
begin
  NextForm:=Form3;
  NextFormShowed:=false;
  Close;
end;