Disgaea Infinite takes players back to the Underworld and features a cast of characters from both
Disgaea and
Disgaea 3. There's no definite place where
Disgaea Infinite takes place in the series' timeline, but considering the play mechanic, "when" it takes place doesn't really matter.
The game opens with a lone Prinny who is tossed out of the window after a bit of a mix up regarding a new pudding shipment and Overlord Laharl. A few hours later, he wakes up only to find Laharl furious over an assassination attempt. Although Laharl recognizes the Prinnies probably don't have anything to do with the plot, he cuts their salaries anyway. Since Prinnies need the money to pay off their sins, they aren't happy.
As luck would have it, you are in possession of a pocket watch that allows you to relive any time in the past. That means you can go back in time and try to set things right. Since you weren't in on the plot in the first place, you have a bit of a mystery on your hands if you want to reclaim your full salary.
Most of Disgaea Infinite's gameplay revolves around watching cut scenes for clues, then rewinding time to influence better outcomes. Throughout the game you'll jump between characters, observing their actions and using possession to nudge them along certain paths. In some respects, gameplay flows like Rashomon or Pulp Fiction. There's no one person to follow the entire time; instead you'll need to follow different characters in order to get the entire story.
The downside to Disgaea Infinite's structure is the amount of repetition. You'll play through sequences multiple times, and though you can skip through them with (X), there's a good chance you'll miss out on an important clue or opportunity to shift the story.