If you decide to load up your Clear Save instead of doing a New Game + you'll start at the save point in Ghardia Shaft, where you can watch the Errand Boys skit. If you head to Lhant Manor and check the star outside you'll get a scene and a minor fight that will reveal a new dungeon, which you can shuttle to.
Accessing the Zhonecage Floors:
In order to participate you'll need to "bet" an item on the pedestal, which will be returned if you complete the floor or lost. The higher the item's resell value, the deeper floor you'll be able to challenge with the 10th floor requiring an item worth approx. 200k.
Note that in order to reach floor 10 you'll need to complete Sidequests No. 64 and floors 1-9 in any order.
The Rules & Treasures:
Each floor consists of 2 different levels with a enemy difficulty counter in the upper right corner that starts at 125%, with a min of 100 and a max of 200, that can lower this by fighting (-10%) or by activating the yellow devices (-25%). The blue devices spawn a random treasure chest, merchant, or monster and each room on a floor has a chest, with the contents varying based on your settings difficulty.
The chests on each floor is based on the character or theme the floor represent. For floors that represent a character you will find Dishes, Weapons, and Unique Equipment specific to that character. For other themed floors you will obtain items specific to that theme. Note that all treasures are random and that each of the floors offers a rare chance of obtaining the permanent stat boots consumables, such as Sage and Savory (sometimes even in the Red version).
Important: Because chests are based on the game difficulty you'll want to generate the floor with a high difficulty, but you can luckily change the difficulty one the floor is generated on that difficulty. This means you can enter the Zhonecage on Chaos and then switch it to Easy to get higher items, without worrying about death to enemies or bosses.