Anthony Rizzo chokes way up when he has two strikes. Could he just use a shorter bat in that situation? That would permit him to have the same basic leverage and have the knob of the bat to push against with his bottom hand. Is there a rule that batters have to keep an intact bat through an at bat? Could a batter have several bats he could use in different situations? e.g. a bunting bat with a fatter barrel, or a short bat for a control situation, etc.
As far as I’m aware, there’s no requirement to use the same bat. There’s nothing in this Wikipedia article specifying using one bat for the whole plate appearance (save a bat breaking from contact).
I’ve seen them break a bat and get another many times.
Yes, you can change bats; no rules against it.
They don’t carry substantially different types of bats for one player largely because it’s a pain in the ass. Rizzo is better off just doing what he’s done for years, rather than learning to use a new bat.
This gives me an opportunity to again bring up the wonderful story of the great Negro League star Norman “Turkey” Stearnes. Stearnes - an truly awesome player, easily one of the five or six best left fielders of all time, very comparable to Carl Yastrzemski - loved his bats, and he did carry several different ones with him at all times, using lighter bats or heavier bats depending on the situation. A pitcher with a really sharp fastball, for instance, would merit a light, quicker bat, while a curveball specialist merited a heavier bat to help Stearnes keep his bat back longer. He had them custom made to his precise specifications, and carried them in specially modified music instrument cases. Sometimes, according to his teammates, they would find him in his hotel room, speaking to his bats, thanking them for big hits or lecturing them if he’d had a bad day.
You didn’t ask to borrow his bats.
Fine story, and one that confirms my suspicions that convenience aside, there might be some advantages in using different bats for different circumstances. Frankly, I wouldn’t be surprised is someone started to do something like that. Remember when Gus Triandos invented a special catcher’s mitt to deal with Hoyt Wilhelm’s knuckler? I think they outlawed it, but the concept of adjusting to circumstances is not unheard of in baseball. They just tend to be slower and more staid in their approach to change.
MLB says
That limits some possibilities, although I’ve heard of some players who switch to lighter weight bats as the season wears on and they get fatigued.
And several players have used so-called bottle bats, for reasons that I’m not totally sure of. Nellie Fox, a favorite of mine when I was a kiddo, used one. He was a great bunter and that may be one reason why he used that type of bat. I’ve often wondered why no one hits with a bat that’s flattened on the front side to some degree. Seems like it might limit the popups that result from slightly undercutting or overcutting the ball. I love the traditions of baseball and the fact that it never changes, but it never changes!
Rules of baseball specify the bat must be round(among other specs).
If you could do that, everyone absolutely would. But you can’t.
Believe me, if there is an advantage to be taken, it will be taken.
Hollowed out ends of bats for the win, anyone? 
If it was a common practice batters might get used to it. But I think it would be a disadvantage to a lot of batters would have difficulty adjusting to the different bats. It would be something to do for outstanding contact hitters who are making all sorts of situational adjustments. I think the average batter is trying much more for consistency in everything they do.
He even kept a few of them in his belfry.