How about a game with more interaction, but based on the same concept?  First player writes a four to seven word alliterative sentence, and the next player completes, adds to, or responds to the first player's sentence, continuing the alliteration, and giving the next player a letter for his/her sentence.
Actually, I do that anyway; spices up the game.
					Actually, I do that anyway; spices up the game.
























 Different New Game
									
									
									Different New Game
								 
							
						 
  
							
						
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