It looks like, in addition to Scrabble Apple, the makers of Scrabble decided to make another game that fuses elements of Bananagrams with those of conventional Scrabble. This one is kind of a Frankenstein hybrid, so don't say I didn't warn you:
The game is divided into rounds. In each round, everyone uses up their tiles by building words on independent mini-Scrabble-boards. Then players score their words, draw new tiles, and continue building up their grids.
Unlike Scrabble Apple, which seemed to be fairly close to Bananagrams, with some Scrabble elements thrown in (scoring and double word score squares), Scrabble Me seems like it is deviating from the Scrabble - Bananagrams continuum. It's more random, in the sense that when someone uses a blank tile (called "wild" in this game), they have to swap their grid with someone else's. However, it is less random in the sense that there is a pool of face-up tiles that one can opt to draw from, instead of from the bag. It somehow reminds me of the card game Uno.
In the interest of trying to categorize these games, I've made this ASCII chart:
D | SCRABBLE SCRABBLE ME
DECOUPLING OF PLAYERS
And there really ought to be a third-dimension where Scrabble Me towers above the others on the Uno-ness axis.
The reviews are sort of favorable though. In spite of the Frankenstein quality, I would like to try this game.