The following list gives alternative ideas for match-three games:
In the Inserting mode, not single tiles but geometric shapes, such as tetrominoes, can be used.
Another idea is to control the mechanics when a player has to push a tile in the direction of the neighbor tile to switch their positions. This game mode can be called Replacement.
A physics-based puzzle can be developed with tile-matching logic and indirect control of elements. Say that the tiles are floating on the surface of water. A player sees a pool in a cross-sectional view; its bottom is not uniform, and there are a lot of ledges of various heights and widths; by controlling the level of water inside the pool, he can put tiles on these ledges (vertical control of elements). By using additional forces, such as waves, the player can move tiles horizontally. Quick wits can help him to arrange tiles in groups that match and eliminate them from the screen.