Can you root for a player without rooting for his team?

This applies to every sport but baseball. I support several players even if I'm rooting against their teams. Likewise, I root against some players even if I want their team to win. Can you do the same for players in other sports?
In baseball a player can do really well or really poorly in a game and still have it not result in a way that reflects their individual performance. In football, I can maybe see this, because there are different groups that play offense and defense. Yet, in basketball it seems that one player can almost singlehandedly change the outcome of the game.

Can you root for a player without rooting for his team?
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