Okay, once upon a time, a very long time ago, in a land far far away, I had a Playstation Two.
And for that Playstation Two, I had an amazing Tetris Game called Tetris Worlds.
ANYWAYS, I have several suggestions for possible Tetrizm modes.
Cascade mode: Tetraminos stay together except when a line clear divides them. When a line clear causes tetraminos to fall, they will continue to fall until each tetramino can't fall anymore. This mode allows for alot of strategy as you can set up a huge cascade that could let you clear 8+ lines with a single piece.
Alternatively, add a setting to turn this mode on or off for all other modes.
Hot-Line mode: Six lines across the matrix will be highlighted, only line clears across these lines will count for any points. Higher highlighted lines are worth more points. These are the lines that are highlighted:
Sticky mode: This mode is similar to Touchdown in that it has preexisting blocks. The ultimate goal is to clear the bottom line. This mode will always be using Cascade, but preexisting blocks won't fall. All of the tetraminos will be made out of randomly colored blocks, a single tetramino could be made out of 4 blocks of 4 different colors. Once a tetramino lands, each separate color is treated as its own block and the tetramino falls apart. The reason this mode is called Sticky Tetris is because if two same colored blocks touch eachother, they stick together and combine into a single block. If a single block is made up of 25 or more small squares(The things tetraminos are made out of), it reaches 'critical mass' and disappears, giving a bonus.
No rotation mode: All the pieces come out in a random orientation and you aren't allowed to rotate them, only move them side to side.