Pillar Chess is a variant of orthodox chess that encorporates elements of the Russian game of Pillar Checkers (Stolbovie shashki) where pieces captured are stacked below the capturing piece. In Pillar Chess, it is the same.
The board and array are those of orthodox chess, except that the pieces are flat tiles or checkers, thus can be stacked and moved as a stack. It it best if the pieces allow their owning player to be determined by looking at their side. However, while the sides are not colored, you could use a magnetic Chess set such as those made by Midnight Snacks Games to play this variant.
The game is conducted by rules of International Chess with the following changes:
If the top piece of the left-behind stack is a Pawn, and the left-behind stack is on the last rank, it does not promote, and it can not move. If the top piece of of the left-behind stack is a Pawn, and the the left-behind stack is on the first or second rank (or a left-behind Pawn moves from the first rank to the second rank), the left-behind stack is entitled to make a double-move, any may be captured en-passant when so doing.
It could be allowed to split a stack so that a piece of the color opposing player is on the top of the portion left behind. This stack would then belong to the opposing player. The same rules about left-behind stacks with Pawns on top apply as with left-behind stacks belonging to the currently moving player; thus you could strand a blocking stack topped by one of your opponent's Pawns on your first rank, and it would stay there, unable to move until you captured it.