A special type of push block. Whenever the player pushes one, all other linked push blocks in the room also move in the same direction unless blocked by a barrier or object. Would be used in puzzle scenarios where you have to manipulate their positioning to press switches on the other side of a barrier, or use the Ice Rod to create your own barricades, and so forth.
Bonus points: Add a color property (red push blocks, blue push blocks, green push blocks, yellow push blocks, etc.) so that there can be multiple distinct groups of linked blocks in one room.