Beat the game first, and at the end, the game will ask you to make a clear data. 
Do so, and save over your existing/last one if you wish. Now load the clear data, 
and you will end up at the Save Plate in the Elza with Hakase/Professor blocking 
the way. There are events and extra dungeons can ONLY be unlocked by this. With 
this, your UMN will also have the map "Omega System".However, even this is like 
an epilogue because you can now trigger all these events and secret dungeons, you 
are still considered to be before the end of the game, before going to the Omega System.