batter switching during an at bat

[dpr528]

Last night I had a coach ask me if his batter could switch from right to left handed batting during an at bat. I told him that once the at bat begins you can't switch unless a new pitcher comes in. I don't even think the kid was a switch hitter and the coach told me that basically he wanted the kid hitting righty while his player stole third and then to move over and hit lefty. I remember that there's a rule that deals with this, but the main thing I can remember is if it's an ambidextrous pitcher and a switch hitter and they keep changing, the ump is to make one of them declare and then stay that way. Was I correct in that the rule is for the batter to remain on the same side of the plate until the at bat ends? I don't have time to look this up this morning and your help would be appreciated. I do have to admit that I thought this coach had a good idea with what he wanted to do, even if it at best skirted the spirit of the rules, and at worst was completely illegal.