bat the ball repeatedly to the air

[ysong]

When two players compete for a rebound (or a pass), one of the players barely reaches the ball and bats it up to the air again. the two players then jump for the second time. That same player reaches the ball again and bats it slightly away from the other player. realizing his height advantage, this player jumps and bats the ball the third time toward a more favorable spot in a very controlled fashion, while his competitors in the vicinity give up and watch his solo play.

Are all those repeated batting legal moves? when does the batting stop being legal, even with defenders in the vicinity?

Thanks.