Backgammon enthusiasts should feel at home with Starz, in which players maneuver pieces around a board according to dice throws, attempting to land on various "power beads." When different beads are added to a piece's spire (which is made of flexible plastic, but still is something to keep away from children), it gains the abilities to move onto red and blue squares, to move diagonally, and to land on opposing pieces. Since a piece acquires the power beads of any opposing piece it captures, everyone has plenty of incentive to play aggressively, even in a four player game.
(Description from Nov. 1984 GAMES Magazine, p. 36, with minor correction--the original read "added to the board's spire," rather than "added to a piece's spire," but the former is clearly incorrect, judging from the picture which accompanies the game description in the magazine; "a piece gains the abilities" was then changed to "it gains the abilities.")