A Stacking Dice Game

Was playing a game, it involved 3 sizes of six sided dice. 36 of each size stacked in a six by six square to start.. The object of the game was to slide the dice of the top level out of the way, so you could slide the dice of the second level out of the way, so you could remove the dice in the bottom level for scoring. The way to move the dice was to slide the smaller dice on top of another die. Each die could hold up to four smaller dice, but their total had to equal the die they were resting on exactly, or less. If the total is less, the dice stay in placed. If the total of the small dice were equal to the die they were sitting on, they can be removed and scored. Once a die was open on the second level, it could be slid next to by any other die on the second level, subject to the same rules as the first level. After that the second level is considered in play and the piles can be moved as though they were a single die. Any small dice on top move with the second level die. If the move allows the small dice a legal move, that move can also be taken. If you move a larger die, any smaller dice on top may also be moved, after the larger die moves.
The second level dice can be removed if they are clear, and they total the number on the bottom level die. To remove a bottom level die it has to be empty, and have at least two empty sides (so initially you only have the bottom four corners eligible to be removed.) Bottom level dice can be slid into any open spot on the bottom level so long as they remain connected to the level.
A player can take a scored die, roll it and attach it back to the pile, but then must immediately move a second level pile to cover it. (Thus you can't reroll any of the top level dice) If this uncovers a legal scoring die, than that die can be scored. This is one way to turn a low scoring die into a higher scoring die. Top level dice are worth their face value, second tier dice are worth 2 times their pips, and the base level are worth 4 times their pips.
If a player cannot move they may pass or roll in a second tier or base level die. There were two games in the dream, one used multicolored dice each tier half the size of the one below it, the other used tiles with a hole in them for the die for the second tier (1") and the base level (2"). All of the dice were the same size in that version. The tiles were clear acrylic so you could see the base below the second level. I think the second version would be a little easier to implement and manipulate.
The game was apparently set up by rolling the dice and placing them in the piles/tiles.