You can manage tasks with flags. For example, this will clear all the activities on top of home.
Intent intent = new Intent(getApplicationContext(), Home.class);
intent.addFlags(Intent.FLAG_ACTIVITY_CLEAR_TOP);
startActivity(intent)
So if you start 4 or 5 or more tasks over the Home Activity, you can call finish on the fifth and get back home.
I am looking forward for a fragment version of it, but it depends on the way you manage tasks.
EDIT
I found it for fragments :
FragmentManager.popBackStack(String name, FragmentManager.POP_BACK_STACK_INCLUSIVE)
Which will pop all states up to the named one.