A batter can change sides of the plate as many times as they choose. Just like a manager can change pitchers as many times as they choose.
Answer.
No a batter cannot change sides, unless the...
Yes, the player may surely switch sides; he may do so as long as the pitcher is not in the "ready position" (see rule 6.06),and, shall be called out if the batter attempts to switch sides during the...
Every batter can change during his bat turn. Only he/she needs to indicate "the change" to the Umpire that he/she will change side and going around the catcher to make that side change.