I would love it if BDM would have the option of one character on Black Spirit Mode, while you play on a second character. This idea came about with the current totem event. I would rather do other options in game than grind for hours on end for fragments.

You mean Tower Trials? Where 5 characters at once, getting items band 10's of millions each upon completion.

When you hit the 3 lines options in the top right, its over with Ruins, Glroy, and for even more xp and items the higher CP each character is, the higher they climb.  You get like 10 to 15 million XP per character with a run.  You may also log into these characters while they are in the Tower, it only pauses the advancement until logged back off.  You may also not upgrade/requip/unequip any items on a character in an active Tower session.